Question

triangle similarity
for each pair of triangles, determine if the triangles are similar (yes) or not (no). if they are similar, then provide by which similarity theorem - sss-, sas- or aa-.
4.
5.
yes □
no □
theorem: ____________
yes □
no □
theorem: ____________
6.
7.
yes □
no □
theorem: ____________
yes □
no □
theorem: ____________
solve for the value of x.

1. $\triangle ngm \sim \triangle egf$
2. $\triangle klm \sim \triangle wvu$

Explanation:

Step1: Analyze Similar Triangles

Since \(\triangle NGM \sim \triangle EGF\), their corresponding sides are proportional. The sides \(GM = 10\), \(GF = 35\), \(NG = x\), and \(EG = 63\) (or we can also use \(NM = 20\) and \(EF = 70\)). Let's use the ratio of \(GM\) to \(GF\) and \(NG\) to \(EG\).

The ratio of \(GM\) to \(GF\) is \(\frac{GM}{GF}=\frac{10}{35}=\frac{2}{7}\).

Step2: Set Up Proportion

Since the triangles are similar, \(\frac{NG}{EG}=\frac{2}{7}\). We know \(EG = 63\), so \(\frac{x}{63}=\frac{2}{7}\).

Step3: Solve for \(x\)

Cross - multiply: \(7x=63\times2\). Then \(7x = 126\). Divide both sides by 7: \(x=\frac{126}{7}=18\).

Answer:

\(x = 18\)