We are asked to prove that the triangles ΔAEB and ΔCDB are congruent.
We are given the following information.
∠A≅∠C
AE ≅ CD
∠BED≅∠BDE
2. Statement: ∠AEB and ∠BED are supplementary.
Notice that the angles AEB and BED form a linear pair meaning that their sum must be equal to 180°.
A linear pair is always supplementary (sum of angles is equal to 180°)
So, the correct reason is "If two angles form a linear pair, then they are supplementary"
3. Statement: ∠CDB and ∠BDE are supplementary.
Notice that the angles CDB and BDE form a linear pair meaning that their sum must be equal to 180°.
A linear pair is always supplementary (sum of angles is equal to 180°)
So, the correct reason is "If two angles form a linear pair, then they are supplementary"
4. Statement: ∠AEB ≅ ∠CDB
5. Statement: ΔAEB ≅ ΔCDB
Notice that we have two pairs of equal angles.
∠A≅∠C and ∠AEB ≅ ∠CDB
Also, we have one equal including side (includein
