# With of the following triangle congruence shortcuts could be used to prove PRQ = TRS 12210203401.jpg Given Data, /_Q ~= /_S bar(QR) ~= bar(SR) a)Side-Side-Side Postulate (SSS) b)Side-Angle-Side Postulate (SAS) c)Angle-Side-Angle Postulate (ASA) d)Angle-Angle-Side Theorem (AAS)

Question
Congruence
With of the following triangle congruence shortcuts could be used to prove PRQ = TRS

Given Data,
$$\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}$$
$$\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}$$
a)Side-Side-Side Postulate (SSS)
b)Side-Angle-Side Postulate (SAS)
c)Angle-Side-Angle Postulate (ASA)
d)Angle-Angle-Side Theorem (AAS)

2020-12-07
Step 1
It is given that,
$$\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}$$
$$\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}$$
$$\displaystyle{I}{n}\triangle{P}{Q}{R}{\quad\text{and}\quad}\triangle{R}{S}{T}$$,
$$\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}$$ (equal angles given)
$$\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}$$ ( equal sides given)
$$\displaystyle\angle{P}{R}{Q}\stackrel{\sim}{=}\angle{S}{R}{T}$$ ( vertically opposite angles)
Here, two angles and one side of both triangle is equal then,
Step 2
$$\displaystyle\triangle{P}{Q}{R}\stackrel{\sim}{=}\triangle{R}{S}{T}$$ (By angle-side-angle congruence)
Hence option C is correct.

### Relevant Questions

Find the triangle congruence (SSS SAS AAS HL)

Given: bar(SQ) and bar(PR) bisect each other.
State the third congruence required to prove the congruence of triangles using the indicated postulate.

a)$$\displaystyle\overline{{{O}{M}}}\stackrel{\sim}{=}\overline{{{T}{S}}}$$
b)$$\displaystyle\angle{M}\stackrel{\sim}{=}\angle{S}$$
c)$$\displaystyle\overline{{{O}{N}}}\stackrel{\sim}{=}\overline{{{T}{R}}}$$
d)$$\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}$$
What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?

A)$$\displaystyle\angle{B}{A}{C}\stackrel{\sim}{=}\angle{D}{A}{C}$$
B)$$\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}$$
C)$$\displaystyle\angle{B}{C}{A}\stackrel{\sim}{=}\angle{D}{C}{A}$$
D)$$\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}$$
State the third congruence required to prove the congruence of triangles using the indicated postulate.

a)$$\displaystyle\overline{{{Z}{Y}}}\stackrel{\sim}{=}\overline{{{J}{L}}}$$
b)$$\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}$$
c)$$\displaystyle\overline{{{K}{L}}}\stackrel{\sim}{=}\overline{{{X}{Z}}}$$
d)$$\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}$$
Select all statements that are true about the triangles.

-Triangle ABC and DCB are congruent by the Angle-Angle Triangle Congruence theorem.
-Triangle ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence theorem.
-Triangle ABC and BCD are congruent by the Side-Side-Side Triangle Congruence theorem.
-Triangle ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence theorem.
-Triangle ABC and DCB are congruent by the Side-Side-Side Triangle Congruence theorem.
-There is not enough information to determine if the triangles are congruent.