Question

question 4 (5 points)
explain how you can determine that each pair of triangles is similar.
6 in.
3 in.
8 in.
4 in.
a angle - angle similarity theorem
b side - side - side similarity theorem
c side - angle - side similarity theorem

Explanation:

Step1: Check the ratio of sides

For the two right - angled triangles, the ratio of the vertical sides is \(\frac{6}{3}=2\), and the ratio of the horizontal sides is \(\frac{8}{4} = 2\).

Step2: Check the included angle

The included angles (the right angles) are equal (\(90^{\circ}\)).
Since the ratios of two pairs of corresponding sides are equal and the included angles are equal, by the Side - Angle - Side (SAS) Similarity Theorem, the two triangles are similar.

Answer:

C. Side - Angle - Side Similarity Theorem