Question

determine if triangle def and triangle ghi are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

triangle def has a right angle at f (90°) and a 54° angle at e. triangle ghi has a 54° angle at h and a 38° angle at g.

answer
attempt 1 out of 2
the triangles dropdown similar.

Explanation:

Step1: Find ∠D in △DEF

Sum of angles in triangle is $180^\circ$.
$\angle D = 180^\circ - 90^\circ - 54^\circ = 36^\circ$

Step2: Find ∠I in △GHI

Sum of angles in triangle is $180^\circ$.
$\angle I = 180^\circ - 54^\circ - 38^\circ = 88^\circ$

Step3: Compare all corresponding angles

△DEF angles: $90^\circ, 54^\circ, 36^\circ$
△GHI angles: $88^\circ, 54^\circ, 38^\circ$
No matching set of three equal angles.

Answer:

The triangles are not similar.