Question

question 5 (23 points)
determine whether each pair of triangles is similar. explain your reasoning.

these triangles ____ similar. i can use the __ similarity theorem. i know that the two legs are ____
i can set up equivalent fractions like $\frac{2.5}{10}=\frac{4.5}{18}$.
if i cross multiply, i can see that $10\cdot4.5=$ ____ and also $2.5\cdot18=$ ____

word bank:
not proportional 45 are angle - angle are not 6...7 proportional wicked long 21 side - angle - side side - side - side 45

Explanation:

Step1: Check similarity

We have two right - angled triangles. For the Side - Angle - Side (SAS) similarity theorem, we check the ratio of the sides.

Step2: Calculate cross - products

For the fractions \(\frac{2.5}{10}=\frac{4.5}{18}\), cross - multiply. \(10\times4.5 = 45\) and \(2.5\times18=45\). Since the cross - products are equal, the ratios \(\frac{2.5}{10}\) and \(\frac{4.5}{18}\) are equal (proportional). Also, the included angles (the right angles) are equal. So, by the Side - Angle - Side similarity theorem, the triangles are similar.

Answer:

are; Side - Angle - Side; proportional; 45; 45