Question

which of the following is not a step in proving triangle similarity using aa? a. identify two pairs of corresponding angles b. show that these angles are congruent c. conclude the triangles are similar d. prove that the triangles are congruent given δxyz - δabc, if xy = 10 cm, yz = 15 cm, and ab = 5 cm, what is the length of bc? a. 15 cm b. 10 cm c. 7.5 cm d. 5 cm which of the following is used to prove that two triangles are similar using aa similarity? a. two pairs of angles b. three pairs of sides c. all angles and all sides d. one pair of sides and one pair of angles

Explanation:

First question

The AA (Angle - Angle) similarity criterion for triangles requires identifying two pairs of corresponding congruent angles to conclude triangle similarity. Proving triangles are congruent is not part of the AA similarity proof steps.

Step1: Set up proportion for similar triangles

Since $\triangle XYZ\sim\triangle ABC$, the ratios of corresponding sides are equal. So, $\frac{XY}{AB}=\frac{YZ}{BC}$.

Step2: Substitute given values

We know $XY = 10$ cm, $YZ = 15$ cm, and $AB = 5$ cm. Substituting into the proportion $\frac{10}{5}=\frac{15}{BC}$.

Step3: Cross - multiply and solve for BC

Cross - multiplying gives $10\times BC=5\times15$, then $10BC = 75$, and $BC=\frac{75}{10}=7.5$ cm.

The AA (Angle - Angle) similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the two triangles are similar.

Answer:

D. Prove that the triangles are congruent

Second question