TODAY IN GEOMETRY…

REVIEW: Properties of Parallelograms

Practice QUIZ 8.1-8.2

Learning Target : 8.3 Prove a quadrilateral is a parallelogram

Independent Practice

Ch.7 RETAKES

1. Opposite sides are congruent.

2. Opposite angles are congruent.

3. Consecutive interior angles are supplementary.

4. Diagonals bisect each other.

PROPERTIES OF PARALLELOGRAMS:

𝐴 𝐵

𝐶𝐷

IN CLASS PRACTICE QUIZ:

• USE WHITEBOARDS in pairs.• Show ALL work.• Box your solutions.

IN CLASS PRACTICE QUIZ SOLUTIONS:

𝟖𝟓°

PROVING A QUADRILATERAL IS A PARALLELOGRAM:

1. Show BOTH PAIRS of opposite sides are parallel (same slope).

2. Show BOTH PAIRS of opposite sides are congruent (same distance).

3. Show BOTH PAIRS of opposite angles are congruent

4. Show ONE PAIR of opposite sides are congruent and parallel (same slope and

distance).

5. Show the diagonals bisect each other.

PRACTICE:

(4) One pair of opposite sides are parallel and congruent

(2) Both pairs of opposite sides are congruent

(3) Both pairs of opposite angles are congruent

EXAMPLE: For what value of x is the quadrilateral a parallelogram?𝐿

5 𝑥−8𝐾

𝑀𝐽3 𝑥

Diagonals of a parallelogram bisect each other(4): Subtract

Divide

PRACTICE: For what value of x is the quadrilateral a parallelogram?

𝑇

8 𝑥−32

𝑆

𝑈𝑅

4 𝑥

Diagonals of a parallelogram bisect each other(4): Subtract

Divide

EXAMPLE: Show that the quadrilateral is a parallelogram.

1. Prove that both opposite sides are parallel:

Slope Slope Slope Slope

2. OR you can find the distance of each opposite sides and show that they are congruent!

𝐹

𝐺𝐻

𝐽

5

5 ¿1¿1

5

5

−12

−12

PRACTICE: Show that the quadrilateral is a parallelogram.

1. Prove that both opposite sides are parallel:

Slope Slope Slope Slope

2. OR you can find the distance of each opposite sides and show that they are congruent!

𝐴𝐵

𝐶

𝐷

HOMEWORK #3:

Pg. 526: 8-14, 19-21, 25-27, 43-47

If finished, work on other assignments:

HW #1: Pg. 510: 3-16, 19, 24-26HW #2: Pg. 518: 3-11, 13-15, 23-31