Warm Up

• Using the parallelogram provided, make as many conjectures as you can about the characteristics of a parallelogram.

Answers to homework pg 7 in packet

Chapter 6.2: Properties of Parallelograms

Students will apply the properties of parallelograms

Definition of a Parallelogram

• a quadrilateral in which both pairs of opposite sides are parallel

Given: ABCD is a parallelogram.Prove:

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AB ≅ CD,AD ≅ CBA B

CDStatements Reasons

1. ABCD is a 1. Given2. Draw BD 2. Through any two points there

exists exactly one line3. AB || CD, AD || CB 3. Definition of parallelogram4. ∠ABD CDB,≅ ∠ 4. Alternate Interior Angles

∠ADB CBD≅ ∠5. DB DB≅ 5. Reflexive Property of

Congruence6. ∆ADB ∆CBD≅ 6. ASA Congruence Postulate7. AB CD, AD CB≅ ≅ 7. CPCTC

Theorem 6.2 If a quadrilateral is a parallelogram, then its opposite

sides are congruent.

Theorem 6.3 If a quadrilateral is a parallelogram, then its opposite

angles are congruent.

Theorem 6.4 If a quadrilateral is a parallelogram, then its consecutive

angles are supplementary.

Theorem 6.5 If a quadrilateral is a parallelogram, then its diagonals

bisect each other.

A B

CD

Practice Problems

Each figure is a parallelogram.

1. VF = 36 cm, 2. What is the perimeter?

EF = 24 cm,

EI = 42 cm

What is the perimeter of NVI?

E VN

IF

x + 3

17x - 3

Let’s Review…

In a parallelogram:

• opposite sides are congruent

• opposite angles are congruent

• consecutive angles are supplementary

• diagonals bisect each other

• http://www.regentsprep.org/Regents/math/geometry/GP9/PracQuadPf.htm