Question

Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, ASA, SAS, AAS, or HL

Answer 1

triangle AEC and ADB
By SAS axiom.

Answer 2

`\triangle ADE \cong \triangle ACB` by SAS.

Explanation:

From the graph, we see that
`\triangle ADE \cong \triangle ACB` by SAS, because
`AE \cong AB`,
`AD \cong AC` and
`\angle EAD \cong \angle BAC`, so by this given elements, we use Side-Angle-Side postulate.

To demonstrate the congruence between angles, we know by given

`m\angle EAC = m\angle BAD`

By sum of angles, we have

`\angle EAC=\angle EAD+\angle DAC\\\angle BAD=\angle BAC+\angle DAC`

Replacing this sum of angles in the first expression, we have

`\angle EAD + \angle DAC = \angle BAC + \angle DAC\\\therefore\angle EAD = \angle BAC`

So, by SAS,
`\triangle ADE \cong \triangle ACB`