Download Ways to Prove that Quadrilaterals are Parallelograms

Ways to Prove that
Quadrilaterals are Parallelograms
Lesson 5.2
Geometry Honors
Page 172
Lesson Focus
There are five ways to prove that a quadrilateral is a
parallelogram.
Four theorems are presented in this lesson that can be used
to show that a quadrilateral is a parallelogram.
Theorem 5.4
If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
Theorem 5.5
If one pair of opposite sides of a quadrilateral are both
congruent and parallel, then the quadrilateral is a
parallelogram.
Theorem 5.6
If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
Theorem 5-7
If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
Examples
Complete with always, sometimes, or never.
1. The diagonals of a quadrilateral _______ bisect each other.
2. If the measures of two angles of a quadrilateral are equal,
then the quadrilateral is _______ a parallelogram.
3. If one pair of opposite sides of a quadrilateral is congruent
and parallel, then the quadrilateral is _______ a
parallelogram.
4. If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is _______ a parallelogram.
5. To prove a quadrilateral is a parallelogram, it is _______
enough to show that one pair on opposite sides is parallel.
Examples
Complete with always, sometimes, or never.
1. The diagonals of a quadrilateral sometimes bisect each
other.
2. If the measures of two angles of a quadrilateral are equal,
then the quadrilateral is sometimes a parallelogram.
3. If one pair of opposite sides of a quadrilateral is congruent
and parallel, then the quadrilateral is always a parallelogram.
4. If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is always a parallelogram.
5. To prove a quadrilateral is a parallelogram, it is never
enough to show that one pair on opposite sides is parallel.
Practice
State the principal definition or theorem that enables you to
deduce, from the information given, that quad. ABCD is a
parallelogram.
B
C
1. BE = ED; CE = EA
2. BAD  DCB; ADC   CBA
3. BC AD; AB DC
4. BC  AD; AB  DC
5. BC AD; BC  AD
E
A
D
Homework
Page 174 - 176
Problems
9, 11, 13, 15, 17, 18, 21, 24