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

1. Given

2. Definition of midpoint

3. Substitution

4. ASA

5. CPCTE

Step-by-step 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

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

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

answer:

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