# To prove:The two triangles are similar using postulate or theorem.

Question
Similarity

To prove:The two triangles are similar using postulate or theorem.
Given information:
The system triangles:

2021-01-20
Calculation:
Consider two triangles WXV and ZXY as shown as in the textbook.
$$\displaystyle\angle{W}{X}{V}\stackrel{\sim}{=}\angle{Z}{X}{Y}$$
They are vertically opposite angles
Compare the corresponding sides, $$\displaystyle\frac{{{W}{X}}}{{{Z}{X}}}=\frac{{10}}{{15}}=\frac{{2}}{{3}}$$
Compare the corresponding sides, $$\displaystyle\frac{{{V}{X}}}{{{Y}{X}}}=\frac{{12}}{{18}}=\frac{{2}}{{3}}$$
Thus,
$$\displaystyle\frac{{{W}{X}}}{{{Z}{X}}}=\frac{{{V}{X}}}{{{Y}{X}}}$$
$$\displaystyle\frac{{2}}{{3}}=\frac{{2}}{{3}}$$
According to the SAS similarity theorem:
Therefore,
$$\displaystyle\triangle{W}{X}{V}\sim\triangle{Z}{X}{Y}$$
Hence, $$\displaystyle\triangle{W}{X}{V}\sim\triangle{Z}{X}{Y}$$ are similar with each other by the SAS similarity theorem

### Relevant Questions

Determine whether the triangles are similar.
If so, write a similarity statement and name the postulate or theorem you used. If not, explain.
To determine:To prove: $$\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}$$ by the SAS similarity theorem.
Given:
The triangles are similar by theorem SAS.
$$\displaystyle\angle{R}=\angle{X}$$ (Given)
To prove:The extended proportions that are needed to prove $$\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}$$ by the SSS similarity theorem.
Given $$\displaystyle\triangle{R}{S}{T},\triangle{X}{Y}{Z}$$ are two triangles.
To determine:Given triangles are similar or not, if not give reason.
Given information:
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)$$\displaystyle\overline{{{O}{M}}}\stackrel{\sim}{=}\overline{{{T}{S}}}$$
b)$$\displaystyle\angle{M}\stackrel{\sim}{=}\angle{S}$$
c)$$\displaystyle\overline{{{O}{N}}}\stackrel{\sim}{=}\overline{{{T}{R}}}$$
d)$$\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}$$
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)$$\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}$$