are the traiangles shown in the diagram at the right similar? Use angle relationships to explain how you know.
A<65
C< 70
B?
F<45
E<115
D< ?

The two triangles have similar angles, thus the two triangles are similar using the AA criteria.
The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are identical, two triangles are said to be congruent. These are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.
For the triangle ABC using the sum of interior angles of triangle we have:
A + B + C = 180
65 + 70 + B = 180
135 + B = 180
B = 45
Now, for triangle DEF we have:
F = 45.
E = 180 - 115 = 65
Thus, D = 70
The two triangles have similar angles, thus the two triangles are similar using the AA criteria.
Learn more about congruent triangles here:
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