1. OBJECTIVE: PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM
LESSON 6.3
PROVING THAT A QUADRILATERAL
IS A PARALLELOGRAM
OBJECTIVE:
Determine whether a quadrilateral is a parallelogram

2. Theorems
Theorem 6.5
If the diagonals of a quadrilateral _______ each other, then the quadrilateral is a parallelogram.
Theorem 6.6
If one pair of opposite sides of a quadrilateral is both _______ and __________, then the quadrilateral is a parallelogram.
bisect
parallel
congruent

3. Theorems Con’t Theorem 6.7 Theorem 6.8
If both pairs of opposite sides of a quadrilateral are __________, then the quadrilateral is a parallelogram.
Theorem 6.8
If both pairs of opposite angles of a quadrilateral are ___________, then the quadrilateral is a parallelogram.
congruent
congruent

4. EXAMPLE #1
Find the values for x and y for which ABCD must be a parallelogram.
If the diagonals of quadrilateral ABCD _______ each other, then ABCD is a parallelogram, so
bisect
10x – 24 = 8x and 2y – 80 = y + 9
2x – 24 = 12
y – 80 = 9
2x = 36
y = 89
x = 18
If x = 18 and y = 89, then ABCD is a ___________.
parallelogram

5. EXAMPLE #2
Determine whether each quadrilateral is a parallelogram. Explain.
a. All you know about the quadrilateral is that only one pair of opposite sides is congruent. Is that enough to prove the quadrilateral is a parallelogram?
__________________________________________________________________________________________________________________
No, b/c there is no theorem that states only one pair of opposite sides must be congruent to be a parallelogram.

6. EXAMPLE #2
Determine whether each quadrilateral is a parallelogram. Explain.
b. The sum of the measures of the angles in a polygon is (n – 2)180, so the sum of the measures of the angles of a quadrilateral is ___________
(4 – 2)180 = 360
If x represents the measure of the unknown angle,
x = ______, so x = _______.
360
105
____________________________________________________________________________
Yes, b/c both pairs of opposite angles are congruent, which makes it a parallelogram.

7. Assignment: pg 307 #1-15, 20-29