Download Conditions for Parallelograms

LESSON
Conditions for Parallelograms
6-3
Lesson Objectives (p. 398):
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Key Concepts
1. Theorems—Conditions for Parallelograms (p. 398):
THEOREM
EXAMPLE
6-3-1
6-3-2
6-3-3
2. Theorems—Conditions for Parallelograms (p. 399):
THEOREM
EXAMPLE
6-3-4
6-3-5
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
131
Geometry
LESSON
Conditions for Parallelograms
6-3
Lesson Objectives (p. 398):
prove that a given quadrilateral is a parallelogram.
______________________________________________________________
______________________________________________________________
Key Concepts
1. Theorems—Conditions for Parallelograms (p. 398):
THEOREM
EXAMPLE
6-3-1 If one pair of opposite sides of a
quadrilateral are parallel and congruent,
then the quadrilateral is a parallelogram.
(quad. with pair of opp. sides and → )
B
C
D
A
6-3-2 If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
(quad. with opp. sides → )
B
C
A
6-3-3 If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
(quad. with opp. → )
D
B
C
A
D
2. Theorems—Conditions for Parallelograms (p. 399):
THEOREM
EXAMPLE
6-3-4 If an angle of a quadrilateral is
supplementary to both of its consecutive
angles, then the quadrilateral is a
parallelogram.
(quad. with supp. to cons → )
6-3-5 If the diagonals of a quadrilateral bisect
each other, then the quadrilateral is a
parallelogram.
(quad. with diags. bisecting each other → )
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
131
B
A
C
x˚
D
B
C
Z
A
D
Geometry
LESSON 6-3 CONTINUED
3. Get Organized In each box, write one of the six conditions for a
parallelogram. Then sketch a parallelogram and label it to show how it meets
the condition. (p 401).
Conditions for
Parallelograms
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
132
Geometry
LESSON 6-3 CONTINUED
3. Get Organized In each box, write one of the six conditions for a
parallelogram. Then sketch a parallelogram and label it to show how it meets
the condition. (p 401).
Conditions for
Parallelograms
Quad. with both pairs
of opp. sides ||
Quad. with diags.
bisecting each other
Quad. with 1 supp.
to both of its consec. ⭄
(180 – x)°
x°
x°
(180 – x)°
Quad. with 1 pair
of opp. sides || and ≅
Quad. with both pairs
of opp. sides ≅
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Quad. with both pairs
of opp. ⭄ ≅
132
Geometry