Question

directions: determine whether the triangles or sas -), and write a similarity stc
1
3
e
f
5
g
r
9
t
15
s
efg~rts
(sas)
3
d
85
a
53°
42°
c
e
b

Explanation:

Step1: Find angles in $\triangle ABC$

In $\triangle ABC$, given $\angle A = 53^{\circ}$ and $\angle ABC=42^{\circ}$. Using the angle - sum property of a triangle ($\angle A+\angle ABC+\angle C = 180^{\circ}$), we find $\angle C=180^{\circ}-53^{\circ}-42^{\circ}=85^{\circ}$.

Step2: Check for angle - angle similarity

In $\triangle ABC$ and $\triangle DBE$, we have $\angle A = \angle DBE = 53^{\circ}$ and $\angle C=\angle BDE = 85^{\circ}$. By the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar by AA similarity.