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Chapter 4: Q5. (page 129)

Describe your plan for proving the following.

Given: CD炉鈯�AB炉;Dis midpoint of AB炉Prove: CA炉鈮�CB炉

Short Answer

Expert verified

CD炉鈮�CD炉(reflexive property)

AD炉鈮�BD炉(D is midpoint)

螖ADC鈮�螖BDC(SAS congruence criteria)

CA炉鈮�CB炉 (corresponding parts of congruent triangles)

Step by step solution

01

Step 1. Show CD¯≅CD¯.

According to reflexive property of congruence, a line segment is congruent to itself.

02

Step 2. Show AD¯≅BD¯.

Using given statement AD炉鈮�BD炉

03

Step 3. Show ΔADC≅ΔBDC.

According to SAS congruence criteria, two triangles are said to be congruent if two sides and including angles of one triangle are congruent to the two sides and including angles of another triangle

So, from step 1, step 2 and m鈭�ADC=m鈭�BDC=90掳

螖ADC鈮�螖BDC

04

Step 4. Show CA¯≅CB¯.

As corresponding parts of congruent triangles are equal

So, CA炉鈮�CB炉

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