Question

what other information do you need in order to prove the triangles congruent using the sas congruence postulate?

a
b
c
d

1. the triangles below are congruent by ___. (sas, aas, hl)

1. in a right triangle, the side opposite the right angle is the longest side and is called the ___. (leg, right angle, hypotenuse)

Explanation:

Question 7

To prove triangles congruent by SAS (Side - Angle - Side), we need two sides and the included angle to be congruent. In the given triangle, we know that \(AC\) is a common side. For \(\triangle ABC\) and \(\triangle ADC\), if \(\angle BAC\cong\angle DAC\) (the included angle between \(AB\) - \(AC\) and \(AD\) - \(AC\)) and \(AC = AC\) (common side), and we can assume \(AB\) and \(AD\) related, but the key is the included angle. Option A is about non - included angles, Option B is a side but not the right side for SAS, Option D is about perpendicularity which is not needed for SAS. So the correct option is C.

The triangles are right - angled triangles. We can see that one leg and the hypotenuse of the right - angled triangles are marked as congruent. The HL (Hypotenuse - Leg) congruence criterion states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the triangles are congruent. SAS requires two sides and the included angle, AAS requires two angles and a non - included side. Here, since they are right - triangles and we have hypotenuse and leg congruence, it's HL.

In a right - triangle, the side opposite the right angle is defined as the hypotenuse. The legs are the sides that form the right angle, and the right angle is the angle, not a side. So the correct term is hypotenuse.

Answer:

C. \(\angle BAC\cong\angle DAC\)

Question 8