In the figure below, which theorem or postulate can you use to prove triangleADM congruent to triangleZMD?
A diagram is shown with two overlapping triangles.Segments A M and Z D are vertical. M D is horizontal.
Segments A D and Z M intersect.
Angle A M D is a right angle. Angle Z D M is a right angle.
Segment A M is marked with 1 hash mark.
Segment Z D is marked with 1 hash mark.
(1 point)
Responses
ASA
ASA
SSS
SSS
SAS
SAS
AAS
The theorem or postulate that can be used to prove triangle ADM congruent to triangle ZMD is SAS (Side-Angle-Side).
To prove triangle ADM congruent to triangle ZMD, you can use the SAS (Side-Angle-Side) theorem. This is because, in the given diagram, there are two pairs of corresponding congruent sides: AM = ZD (both have 1 hash mark) and MD = MD (both are horizontal). Additionally, the right angles at AM and ZD show that the included angles, angle AMD and angle ZMD, are congruent. Therefore, you can use the SAS theorem to prove triangle ADM congruent to triangle ZMD.
To prove that triangle ADM is congruent to triangle ZMD, we need to find a theorem or postulate that matches the given information.
Looking at the diagram, we see that angle AMD is a right angle (90 degrees) and angle ZDM is also a right angle. This tells us that we have a right triangle.
Based on the given information, we can use the SAS (Side-Angle-Side) theorem to prove the triangles congruent.
To use the SAS theorem, we need to show that two corresponding sides and the included angle of the triangles are congruent.
In this case, we have:
- Side AM congruent to side ZM (given, marked with 1 hash mark)
- Side DM congruent to side DM (reflexive property of congruence)
- Angle AMD congruent to angle ZMD (right angle, given)
Therefore, we can conclude that triangle ADM is congruent to triangle ZMD using the SAS theorem.