Question

1. use the diagram to answer the questions that follow:

a. which theorem can be used to determine whether the two triangles are similar?
sss ~
b. if they are similar, complete the similarity statement. if they arent, select \the triangles are not similar\
△jkh ~ △ the triangles are not similar

Explanation:

Part a

Step1: Recall SSS Similarity

SSS (Side - Side - Side) Similarity Theorem states that if the corresponding sides of two triangles are in proportion, then the triangles are similar. We need to check the ratios of the sides of the two triangles.
For triangle \(JKH\), the side lengths are \(JK = 4\), \(KH=5\), \(HJ = 7\). For the other triangle (let's assume the sides are \(LN = 9\), \(NM = 15\), and the third side (let's say \(ML\)) - wait, first, let's list the sides properly. Wait, the first triangle: \(JK = 4\), \(KH = 5\), \(HJ=7\). The second triangle: let's see the sides given are \(LN = 9\), \(NM = 15\), and let's find the ratio of corresponding sides. Let's check the ratios: \(\frac{JK}{LN}=\frac{4}{9}\), \(\frac{KH}{NM}=\frac{5}{15}=\frac{1}{3}\), \(\frac{HJ}{ML}\) (but we don't know \(ML\) yet). Wait, maybe I misread the sides. Wait, the first triangle: \(JK = 4\), \(KH = 5\), \(HJ = 7\). The second triangle: \(LN=9\), \(NM = 15\), and let's check the ratio of \(4\) and \(9\), \(5\) and \(15\) (\(\frac{5}{15}=\frac{1}{3}\)), \(7\) and... Wait, maybe the sides of the second triangle are \(LN = 9\), \(NM=15\), and the third side (let's say \(ML\)) - wait, no, maybe the sides are \(LN = 9\), \(NM = 15\), and \(ML\) (but we need to check the ratios. Wait, \(\frac{4}{9}\approx0.444\), \(\frac{5}{15}=\frac{1}{3}\approx0.333\), \(\frac{7}{x}\) (if \(x\) is the third side). Since \(\frac{4}{9}
eq\frac{5}{15}\), the ratios are not equal. But the question in part a is about which theorem can be used, and the dropdown has SSS ~, which is the SSS Similarity Theorem. So the answer for part a is SSS ~.

Step2: Check for part b

To check if \(\triangle JKH\) is similar to another triangle, we check the ratios of corresponding sides. For \(\triangle JKH\) with sides \(JK = 4\), \(KH=5\), \(HJ = 7\) and the other triangle (let's assume the sides are \(LN = 9\), \(NM = 15\), and let's find the ratio of \(JK\) to \(LN=\frac{4}{9}\), \(KH\) to \(NM=\frac{5}{15}=\frac{1}{3}\), \(HJ\) to (let's say the third side of the second triangle). Since \(\frac{4}{9}
eq\frac{1}{3}\) (because \(\frac{1}{3}=\frac{3}{9}\) and \(4
eq3\)), the sides are not in proportion. So the triangles are not similar.

Answer:

a. SSS ~
b. The triangles are not similar