meesanzheiman16
Answered

Statement Reason

ABCD is a rectangle. Given

Line segment AB and Line segment CD are parallel Definition of a Parallelogram

Line segment AD and Line segment BC are parallel Definition of a Parallelogram

∠CAD ≅ ∠ACB Alternate interior angles theorem

Definition of a Parallelogram

∠ADB ≅ ∠CBD Alternate interior angles theorem

ΔADE ≅ ΔCBE Angle-Side-Angle (ASA) Postulate

Line segment BE is congruent to line segment DE CPCTC

Line segment AE is congruent to line segment CE CPCTC

Line segment AC bisects Line segment BD Definition of a bisector




Which statement can be used to fill in the blank space?

ALine segment AB is congruent to line segment CD

B.Line segment BE is congruent to line segment AE

CLine segment BE is congruent to line segment CE
DLine segment BC is congruent to line segment AD

Verified Answer :

pewter1967

It's D. To prove that line segment BC is congruent to line segment AD, which is the "side" of angle side angle.

lublana

Answer:

D. Line segment BC is congruent to line segment AD.

Step-by-step explanation:

Given ABCD is a rectangle

AB=CD and BC= AD

1.Statement: ABCD  is a rectangle.

Reason: Given

2.Statement:  Line segment AB and line segment CD are parallel

Reason: By definition of parallelogram

3.Statement :  Line segment AD and line segment BC are parallel

Reason: By definition of parallelogram

4.Statement:  \(\angle CAD \cong \angle ACB\)

Reason: Alternate interior angles theorem

5. Statement: \(\angle ADB \cong\angle CBD\)

Reason: Alternate interior angles theorem.

6. Statement :Line segment BC is congruent to line segment AD

7.Statement:  \(\triangle ADE \cong CBE\)

Reason: Angle-Side_ Angle (ASA)

postulate

8.. Statement: Line segment BE is congruent to line segment DE

Reason: CPCT

9. Statement: Line segment AE is congruent to line segment CE

Reason: CPCT

10. Statement: Line segment AC bisects line segment BD

Reason: By definition of a bisector