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- anonymous

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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- anonymous

- schrodinger

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- Loser66

9

- Loser66

You get nothing if you don't make any question on it.

- mathstudent55

Are all the statements given in the problem and you need to supply the missing reasons?

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- anonymous

I am having trouble coming up with the reasons

- mathstudent55

Are the statements given in the problem?

- mathstudent55

Also, do you have a figure?

- anonymous

Yes - all the statements are provided and I just need to provide the reasons. Please see the figure attached. Thanks.

- mathstudent55

|dw:1436807340394:dw|

- mathstudent55

|dw:1436807651551:dw|

- Loser66

Statements Reasons
1. ABCD is a parallelogram : Given
2. AE and CF are perpendicular to diagonal BD: Given
3. AD is parallel to BC: Property of parallelogram
4. Angle ADE is congruent to angle CBF : Alternate interior angles.
5. Angle AED and angle CFB are right angles: given
6. Angle AED is congruent to angle CFB: both are 90 degree from 5
7. AD is congruent to BC: Sides of parallelogram
8. Triangle AED is congruent to triangle CFB: conclusion from4,5,6,7
9. DE is congruent to BF : Result from8
10. EF = 10 and BD = 28: Given
11. BD = DE + EF + FB: From10
12. 28 = DE + 10 + FB: Replace the given information
13. 18 = DE + FB: Minus 10 both sides
14. DE = FB: From 9
15. 18 = 2(DE)
16. 9 = DE = FB : Divide both sides by 2and from14.

- mathstudent55

1. Given
2. Given
3. Definition of parallelogram.
4. Theorem of alternate interior angles of parallel lines
5. Definition of perpendicular lines
6. Theorem: All right angles are congruent
7. Theorem: opposite sides of a parallelogram are congruent
8. AAS
9. CPCTC
10. Given
11. Segment addition postulate
12. Substitution property of equality
13. Subtraction property if equality
14. Definition of congruent segments
15. Substitution
16. Division prop of equality & transitive prop of equality

- anonymous

Can someone help me with the attached proof? The statements are given, I am having problems with the Reasons 5, 6 and 7. Thanks

- mathstudent55

Reason 2: A property of proportions.
In my opinion, there are two statements missing here.
Statement 2a. XR + RQ = XQ Reason 2a. Segment addition postulate
Statement 2b. YS + SQ = SQ Reason 2b. Segment addition postulate
Reason 3. Substitution property of equality
Reason 4. If two triangles have 2 pairs of corresponding sides with proportional lengths and a pair of corresponding congruent included angles, then the triangles are similar.
Reason 6. Definition of similar triangles.
Reason 7. If two lines are cut by a transversal, such that corresponding angles are congruent, then the lines are parallel.

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