Question

show that the triangles are similar and write a similarity statement.

so ( \triangle xyz sim \triangle )

Explanation:

Step1: Identify the equal angles

We are given that \(\angle X = 47^{\circ}\) and \(\angle D=47^{\circ}\), so \(\angle X\cong\angle D\)

Step2: Calculate the ratios of corresponding sides

For \(\frac{XY}{JD}\), \(XY = 21\) and \(JD = 35\), so \(\frac{XY}{JD}=\frac{21}{35}=\frac{3}{5}\)
For \(\frac{XZ}{GD}\), \(XZ = 30\) and \(GD = 50\), so \(\frac{XZ}{GD}=\frac{30}{50}=\frac{3}{5}\)

Step3: Write the similarity statement

By the Side - Angle - Side (SAS) similarity criterion (if an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, the triangles are similar), since \(\angle X\cong\angle D\), \(\frac{XY}{JD}=\frac{XZ}{GD}\), the similarity statement is \(\triangle XYZ\sim\triangle DJG\) (corresponding vertices must be in order)

Answer:

\(\angle X\cong\angle D\), \(\frac{XY}{JD}=\frac{XZ}{GD}\), \(\triangle XYZ\sim\triangle DJG\)