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Chapter 4: Q2. (page 159)

Given: 鈻�MPQ鈮�鈻�PMN; MS炉鈮�PR炉.

Prove: 鈻�MSN鈮�鈻�PRQ.

Short Answer

Expert verified

It is given that 鈻�MPQ鈮�鈻�PMN.

Therefore,鈭�MPQ=鈭�PMN and PQ=MN.

In the triangles鈻�MSN and 鈻�PRQ, it can be noticed that:

鈭�RPQ=鈭�SMN

PQ=MN

MS炉鈮�PR炉

Therefore, the triangles鈻�MSN and鈻�PRQ are the congruent triangles by using SAS postulate.

Therefore, 鈻�MSN鈮�鈻�PRQ.

Hence proved.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

It is given that 鈻�MPQ鈮�鈻�PMN.

Therefore,鈭�MPQ=鈭�PMN and PQ=MN.

03

Step 3. Description of step.

In the triangles鈻�MSN and 鈻�PRQ, it can be noticed that:

鈭�RPQ=鈭�SMN

PQ=MN

MS炉鈮�PR炉

Therefore, the triangles鈻�MSN and鈻�PRQ are the congruent triangles by using SAS postulate.

Therefore, 鈻�MSN鈮�鈻�PRQ.

Hence proved.

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Most popular questions from this chapter

If 螖DEF鈮�螖RST,m鈭�D=100and m鈭�F=40. Name four congruent angles.

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.

Suppose that 螖BIG鈮�螖CAT, then complete the following statement.

__鈮�AT炉

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.

is a common side of two congruent quadrilaterals.
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