Question

1. if △abc≅△def by asa, which of the following pairs of angles are congruent? a. ∠a and ∠f b. ∠a and ∠e c. ∠b and ∠e d. ∠c and ∠d 5. what type of angle is critical in the sas rule? a. the largest angle in the triangle b. the angle closest to the base c. the included angle between two sides d. the angle opposite one side 6. what does sas stand for in geometry? a. side - angle - side - angle b. side - side - angle c. side - angle - side d. side - side - side

Explanation:

Step1: Recall ASA congruence rule

ASA (Angle - Side - Angle) means two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle. So, the corresponding angles are congruent. In \(\triangle ABC\) and \(\triangle DEF\) by ASA, \(\angle B\) and \(\angle E\) are corresponding angles.

Step2: Recall SAS congruence rule for question 5

SAS (Side - Angle - Side) requires that the angle between two sides (the included - angle) of one triangle is equal to the included - angle between the corresponding two sides of another triangle.

Step3: Recall the meaning of SAS in geometry for question 6

SAS stands for Side - Angle - Side in geometry.

Answer:

1. C. \(\angle B\) and \(\angle E\)
2. C. The included angle between two sides
3. C. Side - Angle - Side