Answered: "Decide whether the two triangles must be congruent...."

High School
Geometry
High school geometry
Congruence

nagasenaz

Answered question

2020-11-05

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.

Answer & Explanation

mhalmantus

Skilled2020-11-06Added 105 answers

Given figure is:

Sum of angles in a triangle is $180^{\circ}$ .
$I n △ T P R$
$50^{\circ} + 60^{\circ} + ∠ T R P = 180^{\circ}$
$∠ T R P = 70^{\circ}$
Step 4
$I n △ T S R$ ,
$60^{\circ} + 70^{\circ} + ∠ T R P = 180^{\circ}$
$∠ T R P = 50^{\circ}$
$I n △ T R P and △ T S R$ ,
$∠ T P R = ∠ T S R (E a c h 60^{\circ})$
$∠ P T R = ∠ S T R (E a c h 50^{\circ})$
TR=TR (Common)
Therefore, $△ T P R \tilde{=} △ T S R$ (BY AAS-congruence rule)/
Hence, both triangles are congruent.

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