Question

question 10 of 10
dora drew \\( \triangle j k l \\) and \\( \triangle m n p \\) so that \\( \angle k=\angle n, j k=6, m n=18, k l=4 \\), and
\\( n p=12 \\). are \\( \triangle j k l \\) and \\( \triangle m n p \\) similar? if so, identify the similarity postulate
or theorem that applies.
a. cannot be determined
b. similar - sss
c. similar - aa
d. similar - sas

Explanation:

Step1: Calculate the ratio of the sides

We have \(JK = 6\), \(MN=18\), \(KL = 4\), \(NP = 12\).
The ratio of \(JK\) to \(MN\) is \(\frac{JK}{MN}=\frac{6}{18}=\frac{1}{3}\).
The ratio of \(KL\) to \(NP\) is \(\frac{KL}{NP}=\frac{4}{12}=\frac{1}{3}\).

Step2: Check the included angle

We are given that \(\angle K=\angle N\).

Since we have two pairs of sides in proportion (\(\frac{JK}{MN}=\frac{KL}{NP}\)) and the included angles (\(\angle K\) and \(\angle N\)) are equal, by the SAS (Side - Angle - Side) similarity theorem, the two triangles are similar.

Answer:

D. Similar - SAS