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.