I need help with this proof:
In parallelogram ABCD, AE and CF are perpendicular to diagonal BD, and EF = 10 cm. If BD = 28 cm, then how long are DE and BF?
Given: ABCD is Parallelogram, AE and CF are perpendicular to diagonal BD, EF = 10 cm. BD = 28
Prove: How long are DE and BF
Statements Reasons
1 ABCD is a parallelogram 1 Given
2 AE and CF are perpendicular to diagonal BD. 2 Given
3 AD is parallel to BC 3
4 Angle ADE is congruent to angle CBF 4
5 Angle AED and angle CFB are right angles. 5
6 Angle AED is congruent to angle CFB 6
7 AD is congruent to BC 7
8 Triangle AED is congruent to triangle CFB 8
9 DE is congruent to BF 9
10 EF = 10 and BD = 28 10
11 BD = DE + EF + FB 11
12 28 = DE + 10 + FB 12
13 18 = DE + FB 13
14 DE = FB 14
15 18 = 2(DE) 15
16 9 = DE = FB 16

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