Question

1
is △ xyz ~ △ abc? if so, name which similarity postulate or theorem applies.
image of two triangles, △ xyz with angles at x: 50°, at z: 55°; △ abc with angles at a: 50°, at c: 55°
a. similar - sas
b. similar - sss
c. similar - aa
d. cannot be determined

Explanation:

Step1: Analyze triangle angles

In $\triangle ABC$, $\angle A = 50^\circ$, $\angle C = 55^\circ$. So $\angle B = 180^\circ - 50^\circ - 55^\circ = 75^\circ$. In $\triangle XYZ$, $\angle X = 50^\circ$, $\angle Z = 55^\circ$. So $\angle Y = 180^\circ - 50^\circ - 55^\circ = 75^\circ$.

Step2: Identify similarity postulate

We have two pairs of congruent angles ($\angle A = \angle X = 50^\circ$, $\angle C = \angle Z = 55^\circ$). By AA (Angle - Angle) similarity postulate, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Answer:

C. Similar - AA