# State the third congruence required to prove the congruence of triangles using the indicated postulate. 12210203742.jpg a)bar(OM) ~= bar(TS) b)/_M ~= /_S c)bar(ON) ~= bar(TR) d)/_O ~= /_T

Question
Congruence
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)$$\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}$$

2021-01-11
Given,

Step 2
By using ASA postulate, two angles and included side must be equal.
Here,
$$\displaystyle\angle{N}\stackrel{\sim}{=}\angle{R}$$
$$\displaystyle\overline{{{O}{N}}}\stackrel{\sim}{=}\overline{{{R}{T}}}$$
Therefore the third congruence required is,
$$\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}$$.

### Relevant Questions

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)$$\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}$$

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)$$\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}$$

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)
A Counterexample to the statement, If $$\displaystyle{a}\equiv{b}\pm{o}{d}{m}$$ and $$\displaystyle{c}\equiv{d}\pm{o}{d}{m}$$, where a,b,c,d, and m are integers with c and d positive and $$\displaystyle{m}\geq{2}$$, then $$\displaystyle{a}^{{{c}}}\equiv{b}^{{{d}}}\pm{o}{d}{m}$$.

The postulate or theorem that can be used to prove each pair of triangles congruent.
Given:
The given figure is:

decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.
A Counterexample to the statement, If $$\displaystyle{a}{c}\equiv{b}{c}\pm{o}{d}{m}$$, where a,b,c, and m are integers with $$\displaystyle{m}\geq{2}$$, then $$\displaystyle{a}\equiv{b}\pm{o}{d}{m}$$.
$$\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}$$ ?
a)$$\displaystyle\triangle{D}{B}{C}$$
b)$$\displaystyle\triangle{B}{D}{C}$$
c)$$\displaystyle\triangle{B}{C}{D}$$
d)$$\displaystyle\triangle{D}{C}{B}$$