Question

two fences are intended to be parallel. one fence divides the triangles side into 9 m and 15 m segments, and the other divides the opposite side into 12 m and x segments. what is x to confirm the fences are parallel?
a. 16 m
b. 20 m
c. 17 m
d. 24 m
which of the following is not a criterion for triangle similarity?
a. sss
b. aa
c. sas
d. ssa

Explanation:

Step1: Apply the basic proportionality theorem

If two lines are parallel and intersect two sides of a triangle, the ratios of the corresponding segments are equal. So, we have the proportion $\frac{9}{15}=\frac{12}{x}$.

Step2: Cross - multiply

$9x = 15\times12$.

Step3: Solve for $x$

First, calculate $15\times12 = 180$. Then, $x=\frac{180}{9}=20$.

For the second question:
The SSS (Side - Side - Side), AA (Angle - Angle), and SAS (Side - Angle - Side) are valid criteria for triangle similarity. SSA (Side - Side - Angle) is not a reliable criterion for triangle similarity as it can lead to ambiguous cases.

Answer:

1. b. 20 m
2. d. SSA