Question

R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m∠R = 60, m∠S = 80, m∠F = 60, m∠D = 40, . Are the two triangles congruent? If yes, explain and tell which segment is congruent to

Answer 1

Triangles RST and EFD are similar because they have corresponding angles that are equal. However, without knowing the lengths of their sides, we cannot conclude that they are congruent.

Step-by-step explanation:

To determine if the two triangles are congruent, we can compare their angles. If two triangles have all three corresponding angles equal, then they are similar, but for them to be congruent, they need to have at least one pair of corresponding sides that are equal in addition to the angle similarity.

For Triangle RST, we have the following angles given: m∠R = 60 degrees, m∠S = 80 degrees, and since the sum of angles in a triangle is 180 degrees, m∠T = 180 - (m∠R + m∠S) = 180 - (60 + 80) = 40 degrees. Now looking at Triangle EFD, we have: m∠F = 60 degrees, m∠D = 40 degrees, and again, the third angle would be m∠E = 180 - (m∠F + m∠D) = 180 - (60 + 40) = 80 degrees.

Comparing both triangles, we see that m∠R = m∠F, m∠S = m∠E, and m∠T = m∠D. Hence, the two triangles are similar because they have identical angle measurements, but without information on the sides, we cannot conclude that these triangles are congruent.