Question

determine if triangle lmn and triangle opq are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

triangle lmn has sides: n to m is 16, m to l is 21, l to n is 20.
triangle opq has sides: p to o is 42, o to q is 40, q to p is 32.

answer attempt 1 out of 3

the triangles similar.

Explanation:

Step1: Order the sides of each triangle

For $\triangle LMN$: sides are $16$, $20$, $21$. Order them: $16, 20, 21$.
For $\triangle OPQ$: sides are $32$, $40$, $42$. Order them: $32, 40, 42$.

Step2: Check the ratios of corresponding sides

Calculate $\frac{32}{16}$, $\frac{40}{20}$, $\frac{42}{21}$.
$\frac{32}{16} = 2$, $\frac{40}{20} = 2$, $\frac{42}{21} = 2$.

Step3: Determine similarity

Since all three pairs of corresponding sides are in proportion (ratio = 2), by the SSS (Side - Side - Side) similarity criterion, the triangles are similar.

Answer:

The triangles are similar by the SSS (Side - Side - Side) similarity criterion because the ratios of their corresponding sides are equal ($\frac{32}{16}=\frac{40}{20}=\frac{42}{21} = 2$).