Question

6
is $\triangle abc \sim \triangle def$? if so, identify the similarity postulate or theorem that applies.
(there are two triangles: $\triangle abc$ with $\angle b = 40^\circ$, $ab = 9$, $bc = 15$; $\triangle def$ with $\angle e = 40^\circ$, $de = 3$, $ef = 5$)
a. similar - aa
b. similar - sas
c. similar - sss
d. cannot be determined

Explanation:

Step1: Analyze Angle Condition

In $\triangle ABC$ and $\triangle DEF$, $\angle B = \angle E = 40^\circ$ (given).

Step2: Analyze Side Ratios

For sides around the equal angle:

• In $\triangle ABC$: $\frac{AB}{DE}=\frac{9}{3} = 3$ (assuming $AB = 9$, $DE = 3$ from the diagram's implied lengths).
• In $\triangle ABC$: $\frac{BC}{EF}=\frac{15}{5} = 3$ (assuming $BC = 15$, $EF = 5$ from the diagram's implied lengths).

So, two sides are in proportion and the included angle is equal (SAS Similarity Criterion).

Answer:

B. Similar - SAS