Question

1. is $\triangle abc$ similar to $\triangle dec$ by the angle - angle criterion? explain.

for problems 7 - 9,

• state whether the two triangles are similar by the angle - angle criterion and explain your reasoning;
• if there is not enough information to determine whether the triangles are similar by the angle - angle criterion, explain why not; and
• use some or all of the following vocabulary terms in your explanations.

angle sum of a triangle
vertical angles
alternate interior angles
right angle
linear pair

Explanation:

Step1: Identify congruent alternate angles

$\angle BAC = \angle EDC = 24^\circ$ (alternate interior angles, since $AB \parallel ED$)

Step2: Identify congruent vertical angles

$\angle ACB = \angle DCE$ (vertical angles are congruent)

Step3: Apply Angle-Angle (AA) Criterion

Since two pairs of corresponding angles are congruent, $\triangle ABC \sim \triangle DEC$ by the AA similarity criterion.

Answer:

Yes, $\triangle ABC$ is similar to $\triangle DEC$ by the angle-angle criterion. $\angle BAC$ and $\angle EDC$ are congruent alternate interior angles ($24^\circ$ each), and $\angle ACB$ and $\angle DCE$ are congruent vertical angles. With two pairs of corresponding congruent angles, the AA similarity criterion is satisfied.