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Chapter 4: Q3. (page 129)

Describe your plan for proving the following.

3. Given: WX炉鈮�YZ炉;ZW炉鈮�XY炉Prove: WX炉鈭�ZY炉

Short Answer

Expert verified

ZX炉鈮�ZX炉(reflexive property)

螖WZX鈮�螖YXZ(SSS congruence criteria)

鈭�1鈮�鈭�2 (corresponding parts of congruent triangles)

WX炉鈭�ZY炉(as alternate interior angles are equal)

Step by step solution

01

- Show ZX¯≅ZX¯

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

02

- Show ΔWZX≅ΔYXZ

According to SSS congruence criteria, two triangles are said to be congruent if three sides of one triangle are congruent to the three sides of another triangle

So, from step 1and given

螖WZX鈮�螖YXZ

03

- Show ∠1≅∠2

As corresponding parts of congruent triangles are equal

So, 鈭�1鈮�鈭�2

04

- Show WX¯∥ZY¯

As alternate interior angles are equal then lines are parallel

Thus, WX炉鈭�ZY炉

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

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