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Chapter 4: Q5. (page 132)

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short Answer

Expert verified

螖TRP鈮�螖TRS by ASA (Angle-Side-Angle) Postulate

Step by step solution

01

Step 1. First observation from figure.

Line segmentTR炉 is common in both triangles.

So, by reflexive property of congruency

TR炉鈮�TR炉

02

Step 2. Find ∠TRP.

Since sum of angles of a triangle is 180掳

鈭�TRP+鈭�RPT+鈭�PTR=180掳鈭�TRP+60掳+50掳=180掳鈭�TRP=180掳鈭�110掳鈭�TRP=70掳

03

Step 3. Find ∠RTS.

Since sum of angles of a triangle is180掳

鈭�RTS+鈭�TSR+鈭�SRT=180掳鈭�RTS+60掳+70掳=180掳鈭�RTS=180掳鈭�130掳鈭�RTS=50掳

04

Step 4. Observations from figure and above steps.

鈭�TRPand 鈭�TRSare congruent

So, 鈭�TRP鈮�鈭�TRS

Also, 鈭�PTRand鈭�STR are congruent

So,鈭�PTR鈮�鈭�STR

05

Step 5. Conclude given two triangles are congruent or not.

From step 1 and 4

Two angles and there including side is congruent

Thus,螖TRP鈮�螖TRS by ASA (Angle-Side-Angle) Postulate

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