Title: G-SRT Congruent Triangles
Alignment: HSG-SRT.B. Prove theorems involving similarity
Task:
Using SSS, SAS, ASA, or AAS, determine whether or not the two given triangles are congruent. Give reasoning to support your answer
Commentary:
This task is oriented in a way to get students thinking about the different triangle similarity theorems that they know. SSS, SAS, ASA, and AAS. They will need to use these theorems to determine how these triangles are congruent.
Students will be asked to pick a similarity theorem and use it to help solve the problem. They will be asked to label their triangles to help show the similarity between the two triangles and put together a statement and reason proof to help support their conclusion.
The reason for this task is to show students that just because a shape, in this case a triangle, is shifted, rotated, or reflected, does not mean that the shape has changed. It also helps students use theorems to solve different proofs.
Solution:
By noting the theorems of SSS, SAS, ASA, and AAS we can get a better look at how to prove these triangles are congruent.
- Show the types of congruent triangles
SSS SAS
ASA AAS
- Label the triangle
- Give Statements and Reason to support your answer
Statement Reason
AB EF Equal side length 8
<BAC <FED 90° angles
CA DE Equal side length 6
Therefore SAS congruence.