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.
