Question

Match the following items.

Given: 1 = 2 3 = 4 D midpoint of BC = DE
Prove: A = E
1. ∠1 = ∠2, ∠3 = ∠4, D is midpoint of segment BE, BC = DE Given
2. BD = DE ASA
3. BC = BD Definition of midpoint
4. Triangle ABD congruent to Triangle EBC Substitution
5. ∠A = ∠E CPCTE

Answer 1

I just did this lesson; this answers are right.

1: Given 1: ∠1 = ∠2, ∠3 = ∠4, D is midpoint of segment BE, BC = DE

2: BD = DE 2: Definition of midpoint

3: BC = BD 3: Substitution

4: Triangle ABD congruent to Triangle EBC 4: ASA

5: ∠A = ∠E 5: CPCTE

Explanation:

Answer 2

1. Given

2. Definition of midpoint

3. Substitution

4. ASA

5. CPCTE

Explanation:

1. ∠1 = ∠2, ∠3 = ∠4, D is midpoint of segment BE, BC = DE is given (given).

2. BD = DE, because D is midpoint of BE (definition of midpoint).

3. BC = BD, because you are given that BC = DE and DE = BD, then substitute instead of DE into the first equation segment BD to get BC = BD (substitution).

4. ΔABD≅ΔEBC, because

• BD ≅ BC;
• ∠1≅∠2;
• ∠3≅∠4,

then by ASA theorem ΔABD≅ΔEBC (ASA theorem).

4. Congruent triangles have congruent corresponding parts, then ∠A≅∠E (CPCTE).