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Chapter 5: Q31 (page 170)

Given: ABCD is a 鈻�,CD炉鈮�CE炉

Prove: 鈭�A鈮�鈭�E

Short Answer

Expert verified

It is proved that 鈭�A鈮�鈭�E.

Step by step solution

01

Step 1. Apply properties of parallelogram.

Opposite angles of a parallelogram are congruent.

In 鈻�ABCD, 鈭�Aand 鈭�BCDare opposite angles. Therefore, 鈭�A鈮�鈭�BCD.

02

Step 2. Description of step.

From the given figure, it can be observed that BC炉鈭�AD炉and CD炉is a transversal then 鈭�BCDand 鈭�CDEare alternate interior angles such that, 鈭�BCD鈮�鈭�CDE.

03

Step 3. Isosceles triangle theorem.

If two sides of a triangle are congruent then the angles opposite to those sides are congruent.

Consider 螖CDE, in which CD炉鈮�CE炉then by isosceles triangle theorem, 鈭�CDE鈮�鈭�E

04

Step 4. Description of step.

As 鈭�A鈮�鈭�BCD, 鈭�BCD鈮�鈭�CDEand 鈭�CDE鈮�鈭�Ethen by the transitive property of congruence 鈭�A鈮�鈭�E.

Hence it is proved that 鈭�A鈮�鈭�E.

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