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# Step-by-Step Math Answer

Copy the given figures and label them.

Copy the given figures and label them as shown.

Find
*
m
*
*
C
*
.

The sum of the measures of the angles of a triangle is 180 .

So, to find
*
m
*
*
C
*
, first subtract the sum of
*
m
*
*
A
*
and
*
m
*
*
B
*
from 180
.

180 – (110 + 35 ) = 35

Therefore,

*
m
*
*
C
*
= 35
.

Find
*
m
*
*
P
*
.

To find
*
m
*
*
P
*
, first subtract the sum of
*
m
*
*
Q
*
and
*
m
*
*
R
*
from 180
.

180 – (35 + 35 ) = 110

So,

*
m
*
*
P
*
= 110
.

Compare the corresponding angles of the triangles.

Compare the corresponding angles of the triangles.

*
m
*
*
A
*
=
*
m
*
*
P
*

*
*
*
m
*
*
B
*
=
*
m
*
*
Q
*

*
m
*
*
C
*
=
*
m
*
*
R
*

So, the corresponding angles of Δ
*
ABC
*
and Δ
*
PQR
*
are congruent.

Find the ratio of the corresponding sides.

Find the ratio of the corresponding sides.

Compare the ratios.

Compare the ratios.

Here, the ratios of the corresponding sides are equal.

So, the corresponding sides of Δ
*
ABC
*
and Δ
*
PQR
*
are in proportion.

For similar polygons, all corresponding angles are congruent and the corresponding side lengths are in proportion.

Two polygons are similar, if all corresponding angles are congruent and the measures of all corresponding sides form the same ratio.

For Δ
*
ABC
*
and Δ
*
PQR
*
, the corresponding angles are congruent and the measures of all corresponding sides form the same ratio.

So, Δ
*
ABC
*
and Δ
*
PQR
*
are similar.

Therefore, the response is "yes."