Question

ab / xy = 4 / 2? ac / xz = √52 / √13 △abc ~ △xyz by the sss similarity theorem. which mathematical statement is missing? yz / bc = 6 / 3 ∠b ≅ ∠y bc / yz = 6 / 3

Explanation:

Step1: Analyze SSS similarity theorem

SSS similarity theorem states that if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar.
We have \(\frac{AB}{XY}=\frac{4}{2} = 2\) and \(\frac{AC}{XZ}=\frac{\sqrt{52}}{\sqrt{13}}=\sqrt{\frac{52}{13}}=\sqrt{4} = 2\)

Step2: Check the ratio of the third - pair of sides

For \(\triangle ABC\sim\triangle XYZ\) by SSS similarity, we need \(\frac{BC}{YZ}\) to be equal to the other ratios.
First, find \(BC\): \(B(-4,0)\), \(C(2,0)\), so \(BC=\vert- 4 - 2\vert=6\)
Second, find \(YZ\): \(Y(0,4)\), \(Z(3,4)\), so \(YZ=\vert0 - 3\vert=3\)
Then \(\frac{BC}{YZ}=\frac{6}{3}=2\)

Answer:

\(\frac{BC}{YZ}=\frac{6}{3}\)