Question

Determine whether each pair of figures is similar. Justify your answer.

Answer 1

Answer:

• Δ DEF ≈ Δ BAC because tge corresponding angles of each triangle are congruent. The ratio of the sides is 1.

Explanation:

This table shows the measures of the angles of the triangles BAC and DEG in the same order of vertices as indicated by letters:

Triangle BAC:                                          Triangle DEF

• Measure angle B = 20°                        measure angle D = 20°
• Measure angle A = 120°                       measure angle E = 120°
• Measure angle C = 40°                        measure angle F = 40°

There you see the measure of vertix B is equal to that of vertix D, the measure of vertix A is equal to that of vertix F, and the measure of vertex C is equal to that of vertix F, hence the corresponding vertices are congruents, which means that the triangles are similar.

When you look at the corresponding sides they are also congruent:

Triangle BAC:                                          Triangle DEF

• Length side AB = 6.3                            Length side DE = 6.3
• Length side BC = 8.6                            Length side DF = 8.6
• Measure angle CA = 3.5                       Length side EF = 3.5

Thus, the ratios of the corresponding sides are 6.3/6.3 = 8.6/8.6 = 3.5/3.5 = 1.

Therefore, the last choice shows the correct conclusion about the similarity of that pair of figures: triangles BAC and DEF are similar and the ratio of the corresponding sides is 1.

Answer 2

Each pair of figures is similar to  ''Δ DEF ≈ Δ BAC because the corresponding angles of each triangle are congruent''.

The ratio of the sides is 1.

We have to determine

Whether each pair of figures is similar.

What is the condition for two similar triangles?

If the two sides of a triangle are in the same proportion as the two angles of another triangle, and the angle inscribed by the two sides in both triangles are equal, then the two triangles are said to be similar.

Triangle BAC:                                          Triangle DEF

Measure angle B = 20°                        measure angle D = 20°

Measure angle A = 120°                       measure angle E = 120°

Measure angle C = 40°                        measure angle F = 40°

Triangle BAC:                                          Triangle DEF

Length side AB = 6.3                            Length side DE = 6.3

Length side BC = 8.6                            Length side DF = 8.6

Measure angle CA = 3.5                       Length side EF = 3.5

Therefore,

The ratio of their corresponding sides are;

$\dfrac{ 6.3}{6.3} =\dfrac{ 8.6}{8.6} = \dfrac{3.5}{3.5}=1$

Hence, the ratio of the sides is 1.

To know more about a Similar triangle click the link given below.

https://brainly.com/question/25882965