Question

if two triangles are congruent by asa, what must be true about their corresponding parts? a. their areas are always equal b. only their angles are congruent c. their corresponding angles and sides are congruent d. only their included sides are congruent why is the included side important in asa triangle congruence? a. it ensures the angles form a unique triangle b. it proves that the triangles are equilateral c. it determines the area of the triangles d. it verifies the similarity of the triangles in asa, why must the side be \included\ between the two congruent angles? a. to show that all angles are equal b. to make sure the triangle is unique and congruent c. to ensure that the triangles are similar d. to confirm the triangles are isosceles

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) congruence states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. When triangles are congruent, all corresponding parts (angles and sides) are congruent.

Step2: Analyze first question

Since ASA - congruent triangles have all corresponding parts congruent, this includes both angles and sides. Area equality is a consequence of congruence, but the key fact is the congruence of corresponding angles and sides. So for "If two triangles are congruent by ASA, what must be true about their corresponding parts?", the answer is that their corresponding angles and sides are congruent.

Step3: Analyze second question

The included side in ASA is important because given two angles, the length of the included side ensures that only one unique triangle can be formed. Without the specific length of the included - side, multiple non - congruent triangles with the same two angles could be constructed.

Step4: Analyze third question

The side must be included between the two congruent angles in ASA to make sure that the triangle is unique and congruent. If the side is not the included side, we may not be able to establish congruence, and multiple different triangles can be formed with the given angles and a non - included side.

Answer:

1. c. Their corresponding angles and sides are congruent
2. a. It ensures the angles form a unique triangle
3. b. To make sure the triangle is unique and congruent