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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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