Page 20 - Math Course 3 (Book 2)

Proving a Quadrilateral is a Parallelogram

Given: ΔXVY ≅ ΔZVW and ΔXVW ≅ ΔZVY MO. 7 - L3b
Prove: WXYZ is a parallelogram.
Parallelogram in the
Proof: Since ΔXVY ≅ ΔZVW and ΔXVW ≅ ΔZVY, Coordinate Plane
XY ≅ ZW and WX ≅ YX by CPCTC. By
which method would you prove WXYZ is a
parallelogram? Let’s Begin
A. Both pairs of opp. sides ≅.
B. Both pairs of opp. ∠’s ≅.
C. One pair of opp. sides both ≅ and ||.
D. Diagonals bisect each other Find Measures

Example
Answer

Find x so that the quadrilateral is a parallelogram.
4x – 1
A B

Properties of Parallelograms
Opposite sides of
Which method would prove the quadrilateral is a a parallelogram
parallelogram? are congruent. D C

15 3(x + 2)

AB ≅ DC Opposite sides of a ▱ are ≅.
AB = DC Definition of ≅ segments

4x – 1 = 3(x + 2) Substitution

4x – 1 = 3x + 6 Distributive Property

15 x – 1 = 6 Subtract 3x from each side.
A. Both pairs of opp. sides ||. x = 7 Add 1 to each side.
B. Both pairs of opp. sides ≅.
C. Both pairs of opp. ∠’s ≅.
D. One pair of opp. sides both || and ≅.
Answer When x is 7, ABCD is a
parallelogram.
Answer

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