Triangle Congruence: Finding Missing Data for ABC and DEF with Given Sides 5, 8, 65

Question

What data must be added so that the triangles are congruent?

656565555888555888AAABBBCCCDDDEEEFFF

Step-by-Step Solution

Let's consider that:

DF = AC = 8

DE = AB = 5

8 is greater than 5, therefore the angle DEF is opposite the larger side and is equal to 65 degrees.

That is, the figure we are missing is the angle of the second triangle.

We will examine which angle is opposite the large side AC.

ABC is the angle opposite the larger side AC so it must be equal to 65 degrees.

Answer

Angle ABC equals 65.