Question

determine if triangle jkl and triangle mno are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
triangle jkl: sides jk=20, kl=18, jl=25
triangle mno: sides mn=60, no=54, mo=75, angle at m is 46°

Explanation:

Step1: Match sides to angle

First, identify the sides adjacent to the given angle in $\triangle MNO$: $MN=60$, $MO=75$. In $\triangle JKL$, the sides are $JK=20$, $JL=25$, $KL=18$. We test the ratios of the sides surrounding the potential corresponding angle.

Step2: Calculate side ratios

Compute the ratios of the corresponding sides:
$\frac{MN}{JK} = \frac{60}{20} = 3$
$\frac{MO}{JL} = \frac{75}{25} = 3$
$\frac{NO}{KL} = \frac{54}{18} = 3$
All pairs of corresponding sides have an equal ratio of 3.

Step3: Verify similarity criterion

Since all three pairs of corresponding sides are in proportion (SSS Similarity Criterion), the triangles are similar.

Answer:

The triangles are similar, by the SSS (Side-Side-Side) Similarity Criterion, as all corresponding side lengths are in the equal ratio of $3$.