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

Given information:

The system triangles:

Question

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

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

asked 2021-02-03

Determine whether the triangles are similar.

If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

asked 2020-11-30

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)

Given:

The triangles are similar by theorem SAS.

\(\displaystyle\angle{R}=\angle{X}\) (Given)

asked 2021-02-26

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.

Given \(\displaystyle\triangle{R}{S}{T},\triangle{X}{Y}{Z}\) are two triangles.

asked 2021-02-11

To determine:Given triangles are similar or not, if not give reason.

Given information:

Given information:

asked 2021-03-09

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

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

asked 2021-01-10

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)\(\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}\)

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)\(\displaystyle\angle{O}\stackrel{\sim}{=}\angle{T}\)

asked 2021-02-21

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

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

asked 2021-02-13

decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

asked 2020-12-16

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

asked 2020-10-27

To check: whether the triangles are similar. If so, write a similarity statement.

Given:

The given triangles are:

Given:

The given triangles are: