Quadrilaterals Worksheet With Answers Page 21
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50Examples
1. Given: Quadrilateral ABCD
D
C
DC ≅
AB
DC
AB
Prove: Quadrilateral ABCD is a
A
B
Proof:
Complete the following two-column proof with the appropriate statement or
reason.
Statements
Reasons
1. Quadrilateral ABCD
1. ___________________________
DC ≅
AB
DC
AB
2. ___________________________
2. ∠ CDB ≅ ∠ ABD
3. _______________________
3. Reflexive property
4. ∆ ABD ≅ ∆ CDB
4. ___________________________
AD ≅
5. ___________________________
5.
BC
6. ___________________________
6. Quadrilateral ABCD is a
parallelogram
We now have six ways to prove a quadrilateral is a parallelogram. These are summarized
in the following table. Use these theorems and the definition of a parallelogram to show
that a quadrilateral is a parallelogram.
Ways to Prove a Quadrilateral is a Parallelogram
1. Show opposite sides of a quadrilateral are parallel.
(Definition)
2. Show opposite sides of a quadrilateral are congruent.
(Theorem)
3. Show opposite angles of a quadrilateral are congruent. (Theorem)
4. Show consecutive angles of a quadrilateral are
supplementary.
(Theorem)
5. Show the diagonals of a quadrilateral bisect each other. (Theorem)
6. Show one pair of sides of a quadrilateral are both
congruent and parallel.
(Theorem)
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