Page 18 - Math Course 3 (Book 2)

Proving a Quadrilateral is a Parallelogram
Mo. 7

Lesson 3 CONCEPT SUMMARY

Tests for a Parallelogram

KEY CONCEPTS: 1. Both pairs of opposite sides are parallel.
(Definition)
1. Recognize the conditions that ensure a
quadrilateral is a parallelogram. 2. Both pairs of opposite sides are congruent
2. Prove that a set of points forms a (Theorem 7.9)
parallelogram in the coordinate plane.
3. Both pairs of opposite angle are congruent
(Theorem 7.10)

MO. 7 - L3a 4. Diagonals bisect each other. (Theorem 7.11)

Conditions for Parallelogram 5. A pair of opposite sides is both parallel and
congruent. (Theorem 7.12)

THEOREMS Proving Parallelograms

Example

7.9 If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is parallelogram.

Abbreviation: If both pairs of opp. sides are ≅ ,
then quad, is ▱.

7.10 If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.

Abbreviation: If both pairs of opp. ⦞ are, ≅ ,
then quad, is ▱.

7.11 If the diagonals of a quadrilateral bisects each other,
then the quadrilateral is a parallelogram.

Abbreviation: If both pairs of opp. ⦞ are, ≅ ,
then quad, is ▱.

7.12 If one pair of opposite sides of a quadrilateral is both
parallel and congruent, then the congruent is a
parallelogram.

Abbreviation: If one pair of opp. sides is || and ≅ ,
then quad, is a ▱.

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