Question

1. which postulate or theorem is typically used to establish triangle congruence before applying cpctc?

a. pythagorean theorem
b. midpoint theorem
c. cpctc itself
d. sas postulate

1. in proving congruence, which postulate involves using two angles and the included side?

a. sss
b. hl
c. asa
d. sas

1. why is it important to verify proportionality of sides in sas similarity?

a. to determine the volume of a shape
b. to ensure that the scale factor between the triangles is consistent
c. to measure the perimeter of each triangle
d. to confirm that the triangles have equal angles

Explanation:

1. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used after establishing triangle - congruence. SAS (Side - Angle - Side) postulate is used to prove triangle congruence. Pythagorean theorem is for right - triangle side relationships, midpoint theorem is about mid - points in triangles, and we can't use CPCTC to prove itself.
2. ASA (Angle - Side - Angle) postulate involves using two angles and the included side to prove triangle congruence. SSS is side - side - side, HL is hypotenuse - leg for right triangles, and SAS is side - angle - side.
3. In SAS similarity, verifying proportionality of sides ensures that the scale factor between the triangles is consistent. It has nothing to do with volume, perimeter, or equal angles in the context of similarity based on side - proportion.

Answer:

1. d. SAS Postulate
2. c. ASA
3. b. To ensure that the scale factor between the triangles is consistent