Choose what postulate proves the triangles congruent.
Line AC bisects <BAD, line AC bisects <BCD
A. SSS
B. SAS
C. ASA
D. AAS
E. HL
Looks like ASA to me, but you do not provide any description of the triangles involved.
I just told the quiz AAS
Took**
A. SSS
Why did the triangles go to therapy?
Because they had Sides that were Same in length, and they were congruent!
To determine which postulate proves the triangles congruent, we need to examine the given information.
The statement "Line AC bisects <BAD" means that angle BAD is divided into two equal angles, making them congruent. This can be represented as ∠BAC ≅ ∠DAC.
Similarly, the statement "Line AC bisects <BCD" means that angle BCD is also divided into two congruent angles. This can be represented as ∠BCA ≅ ∠CDA.
Now, let's analyze the answer options:
A. SSS (Side-Side-Side) postulate states that if three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent. This information doesn't provide us with any side lengths, so we can eliminate this option.
B. SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. In this case, we only have the angles bisected by line AC, but no information about side lengths. So, this option can also be eliminated.
C. ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent. Here, we have two pairs of congruent angles (∠BAC ≅ ∠DAC and ∠BCA ≅ ∠CDA) and a common side AC. Therefore, ASA postulate can prove the triangles congruent.
D. AAS (Angle-Angle-Side) postulate states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the triangles are congruent. This doesn't apply to the given information since we don't have congruent sides, so we can eliminate this option.
E. HL (Hypotenuse-Leg) postulate applies specifically to right triangles, where if the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent. Since the given information doesn't involve right triangles, we can eliminate this option as well.
Therefore, the postulate that can prove the triangles congruent based on the given information is C. ASA (Angle-Side-Angle) postulate.