Page 19 - Math Course 3 (Book 2)
P. 19
Proving a Quadrilateral is a Parallelogram
Let’s Begin The shapes in the vest pictured
here appear to be parallelograms.
Describe the information needed
to determine whether the shapes
are parallelograms.
Write a Proof
Example Answer
If both pairs of opposite sides are the same
Write a paragraph proof of the statement: length or if one pair of opposite sides is
congruent and parallel, the quadrilateral is a
If a diagonal of a quadrilateral divides the quadrilat- parallelogram. If both pairs of opposite angles
eral into two congruent triangles, then the quadrilat- are congruent or if the diagonals bisect each
eral is a parallelogram. other, the quadrilateral is a parallelogram.
B C
Determine whether the quadrilateral is a
parallelogram. Justify your answer.
Given: ΔABD ≅ ΔCDB A D
35
Prove: ABCD is a parallelogram 20 20
Proof: Since ΔABD ≅ ΔCDB, AB ≅ CD and 35
BC ≅ DA by CPCTC (Corresponding Parts
of Congruent Triangles are Congruent). Answer
By Theorem 6.9, if both pairs of opposite Each pair of opposite sides has the same
sides of a quadrilateral are congruent, the measure. Therefore, they are congruent. If both
quadrilateral is a parallelogram. Therefore, pairs of opposite sides of a quadrilateral are
ABCD is a parallelogram. congruent, the quadrilateral is a parallelogram.
Properties of Parallelograms
Your Turn!
Example Write a Proof
Write a paragraph proof of the statement:
Some of the shapes in this If two diagonals of a quadrilateral divide the
Bavarian crest appear to be quadrilateral into four triangles where opposite
parallelograms. Describe the triangles are congruent, then the quadrilateral is a
information needed to determine parallelogram.
whether the shapes are parallelograms.
X Y
Answer
If both pairs of opposite sides are the same V
length or if one pair of opposite sides is
congruent and parallel, the quadrilateral is a
parallelogram. If both pairs of opposite angles
are congruent or if the diagonals bisect each
other, the quadrilateral is a parallelogram.
W Z
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