Question

Help with Proofs on quadrilaterals please?

Answer 1

The figure below shows rectangle ABCD.
Rectangle ABCD with diagonals AC and BD passing through point E

The two-column proof with missing statement proves that the diagonals of the rectangle bisect each other.



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




Alternate interior angles theorem

Line segment BC is congruent to line segment AD


Definition of a Parallelogram

∡ADB ≅ ∡CBD


Alternate interior angles theorem

Triangle ADE is congruent to triangle CBE


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 ACbisects Line segment BD


Definition of a bisector


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

∡ABD ≅ ∡DBC

∡CAD ≅ ∡ACB

∡BDA ≅ ∡BDC

∡CAB ≅ ∡ACB

Answer 2

The blank needed filled is for Alternate interior angles theorem I also have a picture

Answer 3

oops wrong photo sorry about that...

Answer 4

it could be
∡BCA is congruent to ∡CAD

Answer 5

I think its CAD ≅ ∡ACB

Answer 6

well..

Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Answer 7

what do you think is right?

Answer 8

We have the same idea, if you didn't notice :D