Question

question 2 of 10
is △abc ~ △lmn? if so, name which similarity postulate or
theorem applies.

a. similar - aa
b. similar - sss
c. similar - sas
d. cannot be determined

Explanation:

Step1: Calculate angle C in △ABC

In a triangle, the sum of angles is \(180^\circ\). For \( \triangle ABC \), we know \( \angle A = 50^\circ \) and \( \angle B = 75^\circ \). So, \( \angle C=180^\circ - 50^\circ - 75^\circ=55^\circ \)? Wait, no, wait the other triangle: \( \triangle LMN \) has \( \angle L = 50^\circ \)? Wait, no, the diagram: \( \triangle ABC \) has \( \angle A = 50^\circ \), \( \angle B = 75^\circ \), so \( \angle C = 180 - 50 -75 = 55^\circ \)? Wait, no, the other triangle \( \triangle LMN \): \( \angle L = 50^\circ \)? Wait, no, the given angles: \( \triangle ABC \): \( \angle A = 50^\circ \), \( \angle B = 75^\circ \). \( \triangle LMN \): \( \angle M = 75^\circ \), \( \angle L = 50^\circ \)? Wait, no, let's recheck. Wait, the problem: \( \triangle ABC \) and \( \triangle LMN \). Let's find angles:

For \( \triangle ABC \):
\( \angle A = 50^\circ \), \( \angle B = 75^\circ \), so \( \angle C = 180 - 50 -75 = 55^\circ \)? Wait, no, maybe I misread. Wait, the other triangle \( \triangle LMN \): \( \angle L = 50^\circ \), \( \angle M = 75^\circ \)? Wait, no, the diagram: \( \triangle ABC \): \( A \) with \( 50^\circ \), \( B \) with \( 75^\circ \), \( C \) is the third angle. \( \triangle LMN \): \( L \) with \( 50^\circ \)? Wait, no, the options are AA similarity. Wait, AA (Angle - Angle) similarity: if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Wait, let's recalculate \( \angle C \) in \( \triangle ABC \): \( 180 - 50 -75 = 55^\circ \). Wait, \( \triangle LMN \): \( \angle L = 50^\circ \), \( \angle M = 75^\circ \), so \( \angle N = 180 - 50 -75 = 55^\circ \)? Wait, no, maybe the angles are \( \angle A = 50^\circ \), \( \angle B = 75^\circ \) in \( \triangle ABC \), and \( \angle L = 50^\circ \), \( \angle M = 75^\circ \) in \( \triangle LMN \). Then, \( \angle A = \angle L = 50^\circ \), \( \angle B = \angle M = 75^\circ \). So by AA (Angle - Angle) similarity, the triangles are similar.

Step2: Check the options

Option A is "Similar - AA", which matches our conclusion. SSS requires all three sides proportional, SAS requires two sides proportional and included angle equal. Since we have two angles equal, AA applies.

Answer:

A. Similar - AA