Name _______________________________________________ Date ________ Lesson 4.8 – Proving a parallelogram CC Geometry Do Now Given vertices of quadrilateral SAND: S(-3, 6) A(6, 0) N(9, -9) D(0, -3)

a. Plot quadrilateral SAND

b. Find the length of each side

SA =

ND =

AN = SD =

c. What do you notice about the lengths of the sides?

d. What type of quadrilateral would you classify SAND as? Conclusions for parallelogram: � ____# ____ because they have the same distance � _______ is a parallelogram because both pairs of opposite sides are congruent

Answer key

To prove a quadrilateral is a parallelogram…show that opposite sides are congruent

A(-3, 6) B(5, 8) C(4, 2) D(-4, 0)

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°¾½

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68)02()44()(

68)86()53()(22

22

CDd

ABd

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37)28()45()(

37)06()43()(22

22

CBd

ADd

**ABCD is a parallelogram because both pairs of opposite sides are congruent 1. Prove the quadrilateral SWIM is a parallelogram.

S(2, 1) W(3, 4) I(9, 6) M(8, 3) 2. Prove that quadrilateral MATH is a parallelogram.

M(3, 2) A(4, 5) T(10, 7) H(9, 4)

AB ≅ CD because they have the same distance

AD ≅ 𝐵𝐶 because they have the same distance

SW = IM and WI = SM because they have the same distance SWIM is a parallelogram because both pairs of opposite sides are congruent

MA = TH and AT = MH because they have the same distance MATH is a parallelogram because both pairs of opposite sides are congruent

3. Prove the quadrilateral QUIZ is a parallelogram. Q(-4, 5) U(5, -1) I(8, -10) Z(-1, -4)

4. Prove ROCK is a parallelogram.

R(2, -2) O(8, -1) C(9, 3) K(3, 2)

QU = IZ and UI = QZ because they have the same distance QUIZ is a parallelogram because both pairs of opposite sides are congruent

RO= CK and RK = OC because they have the same distance ROCK is a parallelogram because both pairs of opposite sides are congruent