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ID: A 1 G CO C 11: Quadrilateral Proofs Answer Section 1 ANS: 2 REF: 011411ge 2 ANS: Because ABCD is a parallelogram, AD CB and since ABE is a transversal, ∠BAD and

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Regents Exam Questions G.CO.C.11: Quadrilateral Proofs Name: ________________________ www.jmap.org 1

G.CO.C.11: Quadrilateral Proofs

1 In the diagram below of quadrilateral , and

are points on and , respectively, , and .

Which conclusion can be proven?

1) 2) 3) 4)

2 Given: parallelogram , diagonal , and

Prove: m

1m2 3 In parallelogram shown below, diagonals

and intersect at .

Prove:

4 Given: is a parallelogram.

Prove: is a rhombus.

5 Given: Quadrilateral with diagonals

and that bisect each other, and 12

Prove: is an isosceles triangle and is

a right triangle

6 Given: Parallelogram ,

, and

Prove: is a rectangle

ID: A 1

G.CO.C.11: Quadrilateral Proofs

Answer Section

1 ANS: 2 REF: 011411ge

2 ANS:

Because is a parallelogram,

and since is a transversal, and 1 are corresponding angles and congruent. If mm2, then m1m2, using substitution.

REF: 060533b

3 ANS:

Parallelogram , diagonals

and intersect at (given). ; (opposite sides of a parallelogram are parallel). (alternate interior angles formed by parallel lines and a transversal are congruent).

REF: 081528geo

4 ANS:

because opposite sides of a parallelogram are congruent. because of the Isosceles Triangle

Theorem.

because of the transitive property. is a rhombus because all sides are congruent.

REF: 011036ge

5 ANS:

Quadrilateral with diagonals

and that bisect each other, and 12 (given); quadrilateral is a parallelogram (the diagonals of a parallelogram bisect each other); (opposite sides of a parallelogram are parallel);

13 and 24 (alternate interior angles are congruent); 23 and 34

(substitution); is an isosceles triangle (the base angles of an isosceles triangle are congruent);

(the sides of an isosceles triangle are congruent); quadrilateral is a rhombus (a rhombus has consecutive

congruent sides); (the diagonals of a rhombus are perpendicular); is a right angle (perpendicular lines form a right angle); is a right triangle (a right triangle has a right angle).

REF: 061635geo

6 ANS:

Parallelogram ,

, and (given); (opposite sides of a are ); (parts of lines are ); (two lines to the same line are ); is (a quadrilateral with both pairs of opposite sides is a ); is a right ( lines form right s); is a rectangle (a with one right is a rectangle).

REF: 061835geo

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