Transcript Lesson 6.3

6-3 PROVING A
QUAD IS A
PARALLELOGRAM
THEOREM
Theorem 6-5: If the diagonals of a quadrilateral
bisect each other, then the quadrilateral is a
parallelogram.
3𝑥 = 𝑥 + 5
−𝑥 − 𝑥
2𝑥 = 5
2 2
5
𝑥 = = 2.5
2
2𝑦 − 7 = 𝑦 + 2
−𝑦
−𝑦
𝑦−7=2
+ 7 +7
𝑦=9
Theorem 6-6: If one pair of opposite sides is both
congruent and parallel, then the quadrilateral is a
parallelogram.
𝑎 + 40 + 𝑎 = 180
2𝑎 + 40 = 180
−40 − 40
2𝑎 = 140
2
2
𝑎 = 70
3𝑐 − 3 = 𝑐 + 1
−𝑐
−𝑐
2𝑐 − 3 = 1
+3
+3
2𝑐 = 4
2
2
𝑐=2
THEOREMS
Theorem 6-7: If both pairs of opposite sides
of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6-8: If both pairs of opposite
angles of a quadrilateral are congruent,
then the quadrilateral is a parallelogram.
5 ways to prove that a quadrilateral is a
parallelogram:
1. Both pairs of opposite sides are parallel (Definition)
2. Diagonals bisect each other (Thm 6-5)
3. One pair of opposite sides are both congruent and
parallel (Thm. 6-6)
4. Both pairs of opposite sides are congruent (Thm. 6-7)
5. Both pairs of opposite angles are congruent (Thm. 6-8)
PRACTICE
• Pg 307-308 #1-15, 26-29