Question

select the two statements that correctly describes this figure.
a the triangle has two congruent sides
b the triangle has two congruent angles
c the triangle has three congruent sides
d the triangle has no congruent sides
e the triangle has no congruent angles
f the triangle has three congruent angles

Explanation:

Step1: Recall triangle properties

In a triangle, if two angles are equal, then the sides opposite those angles are equal. Also, the sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(x\). Then \(x + 73^{\circ}+73^{\circ}=180^{\circ}\), so \(x = 180^{\circ}- 146^{\circ}=34^{\circ}\).

Step2: Analyze each option

• Option A: Since two angles (\(73^{\circ}\) and \(73^{\circ}\)) are equal, by the isosceles - triangle theorem (if two angles of a triangle are congruent, then the sides opposite them are congruent), the triangle has two congruent sides.
• Option B: There are two congruent angles (\(73^{\circ}\) and \(73^{\circ}\)), so this option is correct.
• Option C: We have already found two congruent sides (from the isosceles - triangle theorem), so it does not have three congruent sides.
• Option D: There are two congruent sides (as shown in Step 1), so it does not have no congruent sides.
• Option E: There are two non - congruent angles (\(73^{\circ}\) and \(34^{\circ}\)), so it does not have no congruent angles.
• Option F: Since two angles are \(73^{\circ}\) and the third is \(34^{\circ}\), it does not have three congruent angles.

Answer:

A. The triangle has two congruent sides; B. The triangle has two congruent angles.