What triangle congruence theorem could you use to
prove triangle ADE is congruent to triangle CBE?

Both triangles shown have the congruence line on an angle and an adjacent side. ASA proves congruence because in addition to the angle and side, the triangles ADE and CBE share the same angle on point E. Because the two lines are intersecting, their opposite angles are congruent and the triangles share the opposite angles.

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AFOKE88 AFOKE88 · Answer 2 · 2021-11-05T14:36:20+01:00

The triangle congruence theorem that could be used to show that triangle ADE is congruent to triangle CBE is;

ASA Congruence theorem.

Looking at the given triangles we can say that;

∠AED = ∠CEB

This is because they are both vertically opposite angles and vertically opposite angles are equal.

Now, from the triangle, we are given that;

∠DAE = ∠BCE

We are also given that;

AE = CE

This means that we have 2 corresponding angles and 1 corresponding included side that are congruent.

Thus, the congruence theorem that this represents is ASA Congruence theorem.

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What triangle congruence theorem could you use to prove triangle ADE is congruent to triangle CBE?

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What triangle congruence theorem could you use to
prove triangle ADE is congruent to triangle CBE?