Question

question
determine if triangle abc and triangle def are or are not similar, and, if they are, state how you know.
(note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles similar.

Explanation:

Step1: Find ∠C in △ABC

Sum of angles in a triangle is $180^\circ$.
$\angle C = 180^\circ - 82^\circ - 53^\circ = 45^\circ$

Step2: Compare side ratios (△ABC)

Calculate ratios of adjacent sides to $\angle A$.
$\frac{AC}{AB} = \frac{5}{4}$

Step3: Compare side ratios (△DEF)

Calculate ratios of adjacent sides to $\angle D$.
$\frac{FD}{ED} = \frac{25}{21}$

Step4: Check similarity conditions

$\frac{5}{4}
eq \frac{25}{21}$, and no matching equal angle pairs with proportional sides are found.

Answer:

The triangles are not similar. The ratio of the sides adjacent to the matching $82^\circ$ angles are not equal ($\frac{5}{4}
eq \frac{25}{21}$), and there is no other correspondence of equal angles or proportional sides that satisfies triangle similarity criteria.