Finish the following proof by filling in the blanks.

Reasons: Statements:

1.Segment AC`_|_` segment BD 1._______

2.<AEB and <CEB are rt. angles 2._______

3.`Delta` AEB and `Delta` CEB are rt. `Delta` s 3._______

4.________ 4. Given

5.________ 5.Reflexive Property of Segment Congruence

6.`Delta` ABE`cong` `Delta` CBE 6._______

7.________ 7.Corresponding parts of `cong` Triangles are `cong`

8.________ 8.Definition of Perpendicular Lines

9.________ 9.Definition of a Right Triangle

10. Segment DE`cong` segment DE 10._______

11._______ 11. LL Congruence Theorem

12.Segment AD`cong` segment CD 12.______

### 1 Answer | Add Yours

1. Segment AC is perpendicular to segment BD 1.Given

2. Angle AEB and angle CEB are right angles 2. Definition of

perpendicular lines

3. Triangle AEB and triangle CEB are 3. Definition of right

right triangles triangles

4. Segment AB congruent to Segment BC 4. Given

5. Segment BE is congruent to Segment BE 5. Reflexive

Property of Segment

congruence

6. Triangle ABE is congruent to triangle CBE 6. HL Congruence

Postulate

7. Segment AE is congruent to Segment CE 7. Corresponding

parts of congruent

triangles are congruent.

8. Angle AED and angle CED are right angles 8. Definition of

perpendicular lines

9. Triangle AED and triangle CED are right triangles 9. Definition

of a Right Triangle

10. Segment DE is congruent to DE 10. Reflexive Property of

Segment congruence

11. Triangle AED is congruent to triangle CED 11. LL Congruence

Theorem

12. Segment AD is congruent to CD 12. Corresponding parts of

congruent triangles are

congruent.

**Sources:**

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