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

Answer:

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

Step-by-step 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, $\triangle ADE \cong \triangle ACB$