Given: In quadrilateral ABCD, diagonals AC and BD bisect oneanother.Prove: Quadrilateral ABCD is a parallelogramMatch the statements on the left with the correct reasons on theright to complete the proof.The point you can’t see is Point B.

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TayceeB714237 TayceeB714237 · Answer 1 · 2022-11-03T07:06:10+01:00

a) Definition of bisect

b) Vertcial angles are congruent

c) SAS congruence

d) Converse of Alternate interior angles theorem

e) CPCTC

f) Definition of parallelogram

Explanation:

AC and BD are diagonals that intersect each other. Dividing each diagoanl into equal halves

BP = PD and AP = PC

Reason: Definition of bisect

∠APB and ∠CPD (vertical angles)

∠APD and ∠CPB (vertical angles)

∠APB = ∠CPD, ∠APD = ∠CPB

Reason: Vertcial angles are congruent

ΔAPB = ΔCPD, ΔBPC = ΔDPA

In ΔAPB, we have two sides and one included angle congruent to two sides and one included angle in ΔCPD

Two sides and one included angle of ΔBPC congruent to two sides and one included angle in ΔDPA

Reason: SAS (side-angle-side) congruence

∠ABD = ∠CDP, ∠ADP = ∠CBP

∠ABD and ∠CDP are alternate angles

∠ADP and ∠CBP are alternate angles

Reason: Converse of Alternate interior angles theorem

AB || CD, AD || BC

opposite sides of a parallelogram are parallel

correponding parts of congruent triangles are congruent

Reason: CPCTC

Therefore ABCD is a parallologram

Reason: Definition of parallelogram