Proving a Quadrilateral Is a Parallelogram Answers

Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees.

Given: AD ≅ BC and AD ∥ BCProve: ABCD is a parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent 4. AC ≅ AC 4. reflexive property 5. △CAD ≅ △ACB 5. SAS congruency theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7. parallelogram side theorem What is the missing reason in step 6?

Parallelogram W X Y Z is shown. The length of W X is (2 x + 9) millimeters and the length of W X is (x minus 5) millimeters.

Parallelogram A B C D is shown. The length of A B is (8 x minus 5) inches and the length of D C is (3 x + 10) inches.

Parallelogram L O N M is shown. Diagonals are drawn from point L to point N and from point O to point M and intersect at point Q. The length of line segment O Q is (2 x + 3) centimeters and the length of lines segment Q M is (3 x minus 4) centimeters.

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Given: AB ≅ CD and AD ≅ BCProve: ABCD is a parallelogram. Statements Reasons1.AB ≅ CD;AD ≅ BC1.given2.AC ≅ AC2.reflexive property3.△ADC ≅ △CBA3.?4.∠DAC ≅ ∠BCA; ∠ACD ≅ ∠CAB4.CPCTC5.∠DAC and ∠BCA are alt. int. ∠s;∠ACD and ∠CAB are alt. int. ∠s5.definition of alternate interior angles6.AB ∥ CD; AD ∥ BC6.converse of the alternate interior angles theorem7.ABCD is a parallelogram7.definition of parallelogramWhat is the missing reason in step 3?

Parallelogram P Q S R is shown. The length of P Q is (4 x minus 1) centimeters and the length of R S is (3 x + 7) centimeters.

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x + 3) meters and the length of line segment V S is (2 x minus 7) meters.