Question

Can you conclude from the figure that ABC is similar to DEF? Explain.​

Answer 1

Answer:

Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.

Step-by-step explanation:

We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.

Triangle ABC:

Measure of angle A= 60°

Measure of angle C= 40°

Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°

Triangle DEF

Measure of angle E= 80°

Measure of angle F= 40°

Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°

The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.

The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.

Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.