Q5 of 23 Page 21

In figure 2.22, ray AE || ray BD, ray AF is the bisector of ∠ EAB and ray BC is the bisector of ∠ ABD. Prove that line AF || line BC.

Given ray AE∥ ray BD. ray AF is bisector of ∠ EAB and ray BC is the bisector of ∠ Abd.

To find: line AF ∥ line BC


∠ EAB = 2x (ray AF bisector ∠ EAB)


When a line, shape, or angle inti two exactly equal parts is called bisector.


∠ ABD = 2y (ray BC bisector ∠ ABD)


Ray AE ∥ ray BD and Ab is transversal.


∠ EAD ≅ ∠ ABD (alternate angle) two angle formed when a line crosses two other lines, that lie on opposite side of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.)


2x = 2y


X = y


∠ FAB∠ ABC


But they form a pair of alternate angle that are congruent.


∴ line AF ∥ line BC (hence proved)


More from this chapter

All 23 →
3

In figure 2.20, if ∠ a≅ ∠ b and ∠ x≅ ∠ y then prove that line L ∥ line N.

 4

In figure 2.21, if ray BA || ray DE, ∠ c = 50° and ∠ D = 100°. Find the measure of ∠ ABC.


(Hint: Draw a line passing through point C and parallel to line AB.).

 6

A transversal EF of line AB and line CD intersects the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisectors of ∠ BPQ and ∠ PQC respectively.

Prove that line AB|| line CD.


 1

Select the correct alternative and fill in the blank in the following statements.

If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ............