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?
A. Line segment AB is congruent to line segment CD
B.Line segment BE is congruent to line segment AE
C. Line segment BE is congruent to line segment CE
D. Line segment BC is congruent to line segment AD

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:  [tex]\angle CAD \cong \angle ACB[/tex]

Reason: Alternate interior angles theorem

5. Statement: [tex]\angle ADB \cong\angle CBD[/tex]

Reason: Alternate interior angles theorem.

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

7.Statement:  [tex]\triangle ADE \cong CBE[/tex]

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

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