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If ab parallel to cd ef perpendicular to cd and ∠ged=135°

If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below. Find angle AGE. - 2154619 Transcript. Ex 6.2, 3 In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE. Now, AB || CD & GE is transversal, Hence, ∠. It is given that, AB || CD. EF ⊥ CD. ∠GED = 126º ⇒ ∠GEF + ∠FED = 126º ⇒ ∠GEF + 90º = 126º ⇒ ∠GEF = 36º. ∠AGE and ∠GED are alternate. AB is parallel to CD, and EF is perpendicular to AB. The number of 90 degree angles formed by the intersections of EF and the two parallel lines AB and CD - 843208

Answer to: If line AB is perpendicular to line EF , and line CD is perpendicular to EF , then describe the relation between.. Click hereto get an answer to your question ️ In the given figure, AB∥ CD and CD∥ EF . If BEF = 64^o . Find the value of x,y, Question 3. In Fig. 6.30, if AB || CD, EF ⊥ CD and ∠ GED = 126°, find ∠ AGE, ∠ GEF and ∠ FGE. Solution : ∠GEF + ∠FEG = ∠GED EF ⊥ CD so that ∠ FED. Click hereto get an answer to your question ️ In the given figure AB || CD and CD || EF . Also EA AB . If BEF = 55^∘ find the values of x, y and z

Ex 6.2, 2 In figure, if AB || CD, CD || EF and y: z= 3 : 7, find x. It is given that / = 3/7 y = 3/7 z Let ∠ CON = p Now CD || EF So, p = z Also, y + p. Correct answer to the question AB is parallel to CD , and EF is perpendicular to AB. The number of 90° angles formed by the intersections of EF and the two parallel lines AB and CD is - e-eduanswers.co ∵ CD || EF and a transversal DE intersects them ∴ y + 40° = 180° | Sum of consecutive interior on the same side of a transversal is 180° ⇒ y = 180° - 40. Parallel and Perpendicular 3 September 29, 2014 Determine if segments AB and CD are parallel, perpendicular, or neither: 1. AB formed by (‐2, 3) and (2, 6 Line segment CD is the perpendicular bisector of AB. Statement: line segment AD is congruent line segment DB Line AB is parallel to line CD and is cut by transversal line EF. Statement: 2 and 6, 3 and 7, and 4 and 8 are congruent Reason: If 2 lines are parallel, then the corresponding angles are congruent Statement: angles 3 and 6 and 4.

Download the PDF Question Papers Free for off line practice and view the Solutions online. Currently only available for. Class 10 Class 1 AB is parallel to CD. AC and BD are perpendicular - 17003851 Which values should you plot to show a linear relationship? Day Number of seeds Log(seeds) 1 8 0.903 2 14 1.146 3 22 1.342 4 38 1.580 LO 53 1.724 6 99 Question: 1. In The Figure, AB Is Parallel To CD, EF Is Perpendicular To CD And LGED 126 15 Marks Find I) LAGE. Give Reason. Ii) LGEF And Ii) LFG

Ex 6.2, 3 - In figure, if AB CD, EF ⊥ CD and ∠GED = 126

Class 9 Maths Chapter 6 (Lines and Angles) MCQs are given here online with correct answers. Students can practise these objective questions and test their problem-solving skills. All the multiple-choice questions are based on the latest CBSE syllabus and NCERT curriculum. Solving these chapter-wise problems will help students to score good marks In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to asked Feb 1, 2018 in Class IX Maths by navnit40 ( -4,938 points) circle

In the given figure, If AB CD, EF ⊥ CD and ∠GED = 126º

Parallel lines. Parallel lines are lines with equal slopes. Parallel lines will never intersect each other, because they'll always be the same distance apart. Perpendicular lines. Perpendicular lines have slopes that are negative reciprocals of each other, and they intersect to form 9 0 ∘ 90^\circ 9 0 ∘ angles Math. Draw: 1)Line AB parallel to Ray CD perpendicular to line EF. 2)Line GH perpendicular to line IJ,Line GH perpendicular to Line KL and Line IJ perpendicular to Line KL. 3)Line Segment BC coplanar to Line TS.

ABCD is a trapezium AB parallel to CD. AB=12 and CS=24. What is the length of line EF which is parallel to AB and CD and divides the distance between in the ratio 2:3 To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW In quadrilateral ABCD, AB||DC and AD is perpendicular to AB. If AB=5.2 cm, CD= 3..

Prove that in a ∆ABC, if AD is perpendicular to BC, then AB 2 + CD 2 = AC 2 + BD 2. Solution: Question 73. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided is the same ratio. Using the above result, do the following: In figure, DE|| BC and BD. Suppose, AN and BM are altitudes on CD. AN = BM = h cm, DN = a cm and MC = b cm. So, a + 5 + b = 10 So, a + b = 5(1) In triangle ADN, h^2 = 16 - a^2. (2) In triangle BCM, h^2 = 9 - b^2(3) From (2) and (3), a^2 - b^2 = 16 - 9 = 7 So, (a + b)(a -.. If a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other. Theorem 3.12 If two lines are perpendicular to the same lines, then they are parallel to each other 9 In the diagram below of right triangle ABC, CD is the altitude to hypotenuse AB, CB =6, and AD =5. What is the length of BD? 1) 5 2) 9 3) 3 4) 4 10 Plane A is parallel to plane B. Plane C intersects plane A in line m and intersects plane B in line n. Lines m and n are 1) intersecting 2) parallel 3) perpendicular 4) ske AB g CD g EF g CD g g AB g If two coplanar lines are each perpendicular to the same line, then they are parallel. CD g AB g CD g AB g CD g AB g EF g If two coplanar lines are cut by a transversal so that the interior angles on the same side of the transversal are supplementary, then the lines are parallel. CD g AB g CD g AB g EF g CD g AB g CD.

AB is parallel to! CD and transversal! EF intersects! AB and! CD at G and H, respectively. If mODHG:mOBGH = 1:2, nd mODHG. 4. Which geometric principle is used to justify the construction below? A. A line perpendicular to one of two parallel lines is perpendicular to the other. B. Two lines are perpendicular if they intersect to form congruent. Finally, if, when EF meets JK and CD, it makes the interior angles on the same side less than two right angles, then JK, CD are not parallel, and they will meet on that same side. That is Postulate 5. Some writers however have replaced Postulate 5 with the following, which they think is intuitively simpler: Two intersecting straight lines.

SOLUTION: In quadrilateral ABCD, AB is congruent to CD, AB is parallel to CD, and BF and DE are perpendicular to diagonal AC at points F and how to get CD=7 cm when we will drop two perpendicular lines from D to AB as point E and from C to AB as point F. So,we can see that EF = CD (as the line drawns were perpendicular) Now In triangleADE, We know AD=15 and DE=12 So we can easily find AE = 9 Similarly from triangleBCF, we will get BF = 9cm therefore,EF = AB -(AE+BF) = 25 - 18 =7cm CD 5 1 2 AB 3x 2 2x 5 2x 1 10 2 2x x 5 10 3x 5 2x 1 10 AB 5 4(10) 1 20 5 60 CD 5 3(10) 5 30 Wi 3x 5 1 2 (4x 1 20) Use x to find AB and CD. Subtract 2x from each side. Simplify the right side of the equation. Substitute expressions for the length of each side. hi k Identify CD as the midsegment of kAEB. Use the Triangle Midsegment Theorem. Step. Line perpendicular to HP and parallel to VP PROBLEM 1 A line AB 25mm long is parallel to VP and perpendicular to HP. Point A is 35mm above HP and 20mm in front of VP. Point B is 10mm above Hp. Draw the projections of the line AB

AB is parallel to CD, and EF is perpendicular to AB

  1. #1 Given: ABC CD bisects AB CD AB Prove: ACD BCD Statement 1. ABC 1. Given CD bisects AB CD AB 2. AD DB Side 3. CDA and CDB are right 4. CDA CDB Angle 5. CD CD Side 6
  2. e if JK and LM are parallel, perpendicular, or neither. J (11,-2), K (3,-2), L (1,-7), M (1,-2) perpendicular. 100. If possible, use the Law of Syllogism to make a conclusion. If not possible, choose, no valid conclusion. If a whole number ends in 6, then it is divisible by 2. If a whole number ends in 4, the it is divisible by 2
  3. AB k! CD and! EF intersects! AB at G and! CD at H. If mOAGH = 80 and mODHG = 5x, nd the value of x. 23. In the accompanying diagram, parallel lines! AB and! CD are intersected by! EF at G and H, respectively. If mOAGH = 5x and mOCHG = x +12, nd the value of x. 24. In the accompanying diagram, parallel lines! AB and! CD are intersected by.
  4. 9. Draw a square with 5 cm sides. Hint: first draw a line, longer than 5 cm. Mark two points on it, 5 cm apart. Now. draw two lines perpendicular to your. starting line that go through those points. 10. Find rays, lines, and line segments that are either parallel or perpendicular to each other

Line \(AB\) passes through the point \(A(0;3)\) and has an angle of inclination of \(\text{153,4}\)°. Determine the equation of line \(CD\) which passes through the point \(C(2;-3)\) and is parallel to \(AB\). Determine the equation of line \(EF\), which passes through the origin and is perpendicular to both \(AB\) and \(CD\) In the adjoining figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively. asked Jul 30, 2020 in Triangles by Navin01 (50.7k points) triangles; class-9; 0 votes. 1 answer. In the given figure, 0 is a point inside a ∠PQR such that ∠POR = 90°, OP = 6 cm and OR= 8 cm. If PQ. Draw EF and GH perpendicular to CD; then EF will be equal to GH. For, the straight line AB meets the two straight lines This implies that the parallel lines AB and CD are everywhere the same distance apart. This could also be proved by showing that EG, FH are equal, and 15. then citing I. 33 If two lines are perpendicular to each other, then the product of their slopes is equal to - 1.The figure below shows, the lines AB and CD are perpendicular to each other. Further on you'll learn to find if the lines are parallel or perpendicular in the given case and their properties

Name a street that appears to be parallel to S 17th Street. 18. MATHEMATICAL PRACTICE 4 Use Diagrams Name a street that appears to be parallel to Vernon Street. 19. Name a street that appears to be perpendicular to S 19th Street. 20. SMARTER Choose the labels to make a true statement. IJ GH ‹ ___ › ‹ __ › AB ‹ ___ › is perpendicular. Name: Super Teacher Worksheets - www.superteacherworksheets.com Parallel, Intersecting, and Perpendicular A B C D Parallel Lines AB and CD are parallel lines. They. Parallel lines are always the same distance apart: they never meet. On drawings, parallel lines are shown with arrows. If there is more than one pair of parallel lines on a drawing, then the arrows are doubled up for the second pair. Perpendicular lines are shown with a square for the angle, rather than a curve AB BC CD AD AB BE EF AF Hence, the perimeter of the gm is greater than the perimeter of the rectangle. EXAMPLE 28 M and N are points on the side PR of the triangle PQR such that

If line AB is perpendicular to line EF , and line CD is

In a trapezium ABCD with AB = 20 cm, CD = 10 cm, AM parallel to CD, P and Q are the mid point of AC and BD then the length of PQ is Lines and Angles Class 9. Q1 : In the given figure, lines AB and CD intersect at O. If and find ∠BOE and reflex ∠COE. Q2 : In the given figure, lines XY and MN intersect at O. If ∠POY = and a:b = 2 : 3, find c. Let the common ratio between a and b be x. XY is a straight line, rays OM and OP stand on it

In the given figure, AB∥ CD and CD∥ EF

  1. g a linear.
  2. staff. 01/04/2020 11:20 PM. Mathematics. 1 Answers
  3. 1.> The parallel lines intersect each other at infinity. 2.>For two parallel lines all points of one line are equidistant from another line. 3.>All straight lines which are parallel to one straight line will be parallel to all the lines to which first line is parallel. 4.>It s adopted that an angle between parallel straight lines is equal to zero

Question 3. In Fig. 6.30, if AB CD, EF ? CD and ? GED ..

  1. Steps: Line CD C D is intersected with line P P, hence the vertically opposite angles so formed are equal. y =130∘. y = 130 ∘. Similarly, line AB A B is intersected by line P P hence the sum of adjacent angles formed is 180∘. 180 ∘. We know that, if a transversal intersects two lines such that a pair of alternate interior angles is.
  2. Symbols in Geometry Common Symbols Used in Geometry. Symbols save time and space when writing. Here are the most common geometrical symbols
  3. g a straight path, extending in both directions. It does not have a beginning or an end. A line segment is a part of a line, defined by two endpoints. A ray is a part of line that has only one endpoint, and extends indefinitely in one direction
  4. e all angles form 1 to 8
  5. The perpendicular bisector of the line segment $\overline {AB}$ is the line that passes through the midpoint of $\overline {AB}$ and is perpendicular to $\overline {AB}$. The equation of the perpendicular bisector of the line segment joining the points (1,2) and (-5,12) is. 24,391 results
  6. When one line forms two equal angles where it meets another line, the two lines are said to be perpendicular. Because the two equal angles are angles on a straight line, their sum is 180°, hence each angle is 90°. In the figure below, lines AB and CD intersect at point M. In this chapter, you are required to give good reasons for every.
  7. NCERT Exemplar Class 9 Maths Chapter Exercise 6.4. Question 1. If two lines intersect, prove that the vertically opposite angles are equal. Solution: Let the two lines AB and CD intersect at a point O. Since, ray OA stands on line CD. ∴ ∠AOC + ∠AOD = 180° [Linear pair]. (i) Since, ray OD stands on line AB

In the given figure AB CD and CD EF

Parallel and Perpendicular Lines Use the coordinate plane above to accurately graph the following: o Plot Point A (-5, 8) o Graph a line through point A with a slope of -2/3. Label another point on the line, point B. o Plot Point C (8,-4). o Graph a line parallel to AB that passes through Point C. Label another point on the line, point D Study Guide Review 205 Write the equation of each line in the given form. 30. the line through (6, 1) and (-3, 5) in slope-intercept form 31. the line through (-3, -4) with slope _2 3 in slope-intercept form 32. the line with x-intercept 1 and y-intercept -2 in point-slope form Determine whether the lines are parallel, intersect

A vertical line segment is drawn through the circle's intersection at points C and D. A horizontal line segment passes through a point on the left side of circle A labeled E and centers A and B. Radii A C, A D, B C and B D and chords E C and E D are drawn.</p>. (From Unit 1, Lesson 2. A sheet of paper with points and is folded so that and match up with each other. Explain why the crease in the sheet of paper is the perpendicular bisector of segment . (Assume the conjecture that the set of points equidistant from and is the perpendicular bisector of segment is true.) (From Geometry, Unit 1, Lesson 3.

Y7 -Summer -Block 1 -Step 5 -Measure angles up to 180°Answers Question Answer 1 a)70° b)125° c) 160° d)93° 2 a)The angle is an obtuse angle so is more than 90°. b)She has read the scale from the wrong end of the protractor The radius of each of these arcs must be more the half the length of AB. Let these arcs cut each other at points C and D. Join CD which cuts AB at M Then AM = BM. Also ∠AMC = 90° Hence, the line segment CD is the perpendicular bisector of AB as it bisects AB at M and is also perpendicular to AB. Question 2 In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB. Prove that : (i) BD = CD (ii) ED = EF. Answer. AP and BQ are equal and parallel to each other. If AD and BC are on different sides of AB prove that CD bisects AB. Answer Question 17 Q1 Identify the pairs of parallel line segments in the figure. A.AB and CD, EF and GH. B.AB and GH, CD and EF. C.AB and EF, CD and GH. D.None of the abov Note that this does not make CD and EF critically parallel to each other. The P-line AB has two collections of critical parallels, one at each direction at infinity. Drag EF so that it is critically parallel to both the other lines and so that the 3 lines form a triangle with vertices at infinity

Ex 6.2, 2 - In figure, if AB CD, CD EF and y:z = 3:

Best Answer. #4. +1468. +4. Line segment EF is parallel to the line segment CD. Both line segments have the same lengths ( 8 units ). They are 1 unit apart from each other. And finally, these line segments create an inscribed rectangle with side lengths of 8 and 1 unit. A diagonal of this rectangle is the diameter of a circle Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchang In the following diagram it is known that segment AC is parallel to segment BD and segment AB is parallel to segment CD. it is known that line ABC and line EF bisects line AC at B. Which of the following cannot be concluded from these givens? segment AD is perpendicular to ray BA , and segment CD perpendicular to ray BC 1. In the accompanying diagram, line ' is parallel to line m, and lines s and t are transversals that intersect at a point on line m. Which statement must be true? A. mO1 = mO4 B. mO4 = mO2 C. mO1 = mO2 + mO3 D. mO5 = mO2 + mO3 2. In the accompanying diagram,! AB k! CD, and! EF is a transversal that intersects! AB at G and! CD at H In the given figure AB parallel CD and EF is a transversal cutting them at G and H respectively if angleEGB=35 and QP perpendicular EF then find anglePQH. Share with your friends. Share 0. Dear student, Your question is unclear as the figure is missing from it, kindly provide the figure, so that we could clear your doubt..

AB is parallel to CD , and EF is perpendicular to AB

8.1n the diagram below of circle O, diameter AB is perpendicular to chord CD at E. If AO = 10 and BE = 4, find the length of CES 9.1n circle R shown below, diameter DE is perpendicular to chord ST at point L Parallel and Perpendicular Lines Chapter Test Form A Circle the best answer. 1. Classify AB and CD. A skew segments B parallel segments C perpendicular segments D intersecting segments Use the figure for Exercises 2-4. 2. How are line m and line s related? A intersecting C perpendicular B parallel D skew 3. Identify the transversal. A line m. CD intersects hypotenuse AB at D. 15 Line segment CD is the altitude drawn to hypotenuse EF in right triangle ECF. If EC =10 and EF =24, then, to the nearest tenth, ED is 1) 4.2 the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station AB: AD?:AE. Which replaces the ? to make the statement true? A AC B AE C DE D BC 1 Which of the following is the measure of the supplement of ∠CAB? A 42 B 90 C 132 D 142 2 Two parallel sections of pipe are joined with a connecting pipe as shown. What is the value of x? F 90 G 115 H 135 J 160 3 Parallel lines l and m are cut by. 2.5 pg 36 and 38 ANSWERS.notebook 1 October 31, 2018 CD, EF, HG AE, BF, EH, FG 1. Name all segments parallel to AB . 2. Name all segments skew to CD . DO NOW..

In figure, AB CD and CD EF

Perpendicular Transversal Theorem - In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. b||c and a ⊥b Given ∠1 is a 90o angle Definition of Perpendicular Lines ∠1≅∠2 Parallel Lines Postulate m∠2 is 90o Transitive Property a ⊥c Definition of Perpendicular Line Two chords AB and CD of a circle are parallel and a line L is the perpendicular bisector of AB. asked Mar 9, 2019 in Class X Maths by muskan15 ( -3,986 points) circle h the diagram of circle O, diameter AB is perpendicular to CD at E. Vthich of the following three statements is true? 1. CE=ED 11 CB=BD 11 AC B 1, 11, and 111 A) l, only D) land Il, only C) lard Ill, only h àccompanying diagram of circle O, chords AB and CD intersect at E, AE = x, EB = x + 1, =x-l, and ED = 2x. Find AE. EH 8-2- Example 3C: Determining Whether Lines Are Parallel, Perpendicular, or Neither Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. CD and EF for C(-1, -3), D(1, 1), E(-1, 1), and F(0, 3) The lines have the same slope, so they are parallel

13 14 In the triangle shown, Which statement is true about the angles in F is the greatest G is the greatest H is the least J mG∠ is the least mR∠ mG∠ mR∠ RGB? B G R 78 11 GR BR BG== =11 8 7and . 15 Consider the following statement. Which is the inverse of the statement In Figure,if line segment AB is parallel to the line segment CD, what is the value of ?12 (b) 15(c)1... AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB

Geometry Multiple Choice Regents Exam Questions www.jmap.org 3 13 Which line is parallel to the line whose equation is 4x +3y =7 and also passes through the point (−5,2)? 1) 4x +3y =−26 2) 4x +3y =−14 3) 3x +4y =−7 4) 3x +4y =14 14 In a given triangle, the point of intersection of th This quiz is incomplete! To play this quiz, please finish editing it. 20 Questions Show answers. Question EF is perpendicular to both AB and DC which are parallel tangents. Parallel tangents can only be at the ends of a diameter to the circle. Now, from symmetry, E and F are midpoints of AB and CD

CD is perpendicular to GH Ans: _____ 6. AB is parallel to EF. Ans: _____ True False False True . www.jimmymaths.com 3 | P a g e Refer to the diagram below for Question 7 and 8. 7. Which one of the letters has parallel lines? Ans: _____ 8. Which letter(s) has/have perpendicular lines?. Parallel Lines. Author: amshows, anders84. Lines AB and CD are parallel. Line EF is a transversal that cuts lines AB and CD. 1. What things do you notice about the angles formed by the transversal EF and the parallel lines? 2. Corresponding angles are angles created by a transversal and are at the same location at each intersection of two lines 100 Geometry Problems David Altizio Page 4 31.For an acute triangle 4ABC with orthocenter H, let H A be the foot of the altitude from A to BC, and de ne H B and H C similarly. Show that H is the incenter of 4H AH BH C. 32.[AMC 10A 2013] In 4ABC, AB = 86, and AC = 97 1. In the following figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE. Ans. Since AB is a straight line, ∴ AB and CD intersect at O. Thus, ∠BOE = 30° and reflex ∠COE = 250. 2. In the following figure, lines XY and MN intersect at O

Geometry Proofs: Givens, Statements and Reasons - Quizle

In the given figure AB is parallel to CD;CD is parallel to EF and y:z=3:7 find x Answers: 3 Get ### Other questions on the subject: Math. Math, 18.08.2019 00:00, dhvani6272. Find the smallest number which when diminished by 7. Answers: 3. continue. Math, 18.08.2019 05:00, gyanendra19. In a village, every weekend, three-eigth of the men and one. Let CD and EF denote the two common tangents that cross PQ between P and Q, with C and E belonging to M and D and E belonging to N. Finally, let G and H be the intersections of CD and EF with AB respectively. Show that angles PGQ and PHQ are both right angles. 83 Chapter 8: Lines And Angles Exercise - 8.4 Question: 1. In below fig. AB CD and ∠1 and ∠2 are in the ratio 3: 2. Determine all angles from 1 to 8

In the Given Figure, Ab and Cd Are Parallel Lines and Transversal Ef Intersects Them at P and Q Respectively. If ∠Apr = 25°, ∠Rqc = 30° and ∠Cqf = 65°, The If we are given two line segments, AB and CD, we can construct a rectangle with both AB and CD sides of length. Suppose CD is the shorter of the two. First, we create a line AE perpendicular to AB at A. Then, cut off a segment of AE equal in length to CD. We will call this point F. Now, we can create two new perpendicular lines CD ¯˘, GH ¯˘, and EF ¯˘ are all parallel to AB ¯˘, but only CD ¯˘ passes through D and is parallel to AB ¯˘. b. BC ¯˘, AD ¯˘, AE ¯˘, and BF ¯˘ are all perpendicular to AB ¯˘, but only AD ¯˘ passes through D and is perpendicular to AB ¯˘. c. DG ¯˘, DH ¯˘, and DE ¯˘ all pass through D and are skew to AB ¯˘. d.

In figure, if AB CD, CD EF and y : z = 3 : 7, find x

ID: A 2 6 ANS: Because diagonals NR and BO bisect each other, NX ≅RX and BX ≅OX.∠BXN and ∠OXR are congruent vertical angles. Therefore BNX ≅ ORX by SAS. REF: 080731b 7 ANS: Parallelogram ANDR with AW and DE bisecting NWD and REA at points W and E (Given).AN ≅RD, AR ≅DN (Opposite sides of a parallelogram are congruent).AE = 1 2 AR, WD = 1 2 DN, so AE ≅WD (Definitio EF is a transversal of AB and CD. 5 If a point is on the bisector of an angle. Through a given point not on a given line, one and only one line can be drawn parallel to a given line. 10 if PA=PB then P is on CD, the perpendicular bisector of AB. 28 Interior Angles Given AB and CD are parallel lines and EF is the transversal intersecting AB and CD at 'X' and 'Y'. ∠ 1, ∠ 3 are one pair of alternate interior angles and ∠ 2, ∠ 4 are another pair of alternate interior angles. It is required to prove that ∠ 1 = ∠ 3 and ∠ 2 = ∠ 4. We have ∠ 1 = ∠

AB is parallel to CD

AB and CD are parallel, and BD is a diameter of the circle. If mAD= 60, what is mOCDB? A. 20 B. 30 C. 60 D. 120 51. In the accompanying diagram of circle O, chords AB and CD intersect at Eand AD is a diameter. If m CB = 82, nd mOAED. 52. In the accompanying diagram of circle O, chord AB is parallel to chord CD. If m (AC = 100, nd mOBOD. 53 Exercise 4.1: Lines and Triangles. Question 1: In the given figure, AB is a mirror. PQ is the incident ray and QR, the reflected ray. If , find . Ans: We know that the angle of incidence = angle of reflection. Hence, let. Since, AQB is a straight line, we have

Draw another line segment, CD, parallel to AB. Solution Use a ruler to draw a line segment. Label its endpoints A and B. Place the edge of a right triangle along AB as shown. Place a ruler against the bottom edge of the triangle. Slide the triangle along the ruler. Draw along the perpendicular edge of the triangle to create a line parallel to AB It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2. Let. In the figure angle 1 and 2 are supplementary. So, 3x + 2x = 180 ⇒ 5x = 180 ⇒ x = 36 ∠ 1 = 36 × 3 = 108 ° and ∠ 2 = 36 × 2 = 72 ° Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so. Since, angles 1 and 3 and 2 and 4 are. Construct Parallel Lines - Explanation and Examples. Constructing a line parallel to a given line that goes through a given point involves knowing some facts about parallel lines and copying angles. To do this, we will need to construct a transversal. This is a line that crosses two parallel lines. Several pairs of equal angles are created.

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