Holt McDougal Geometry

6-4 Properties of Special Parallelograms
6-4 Properties of Special Parallelograms
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Objectives
Prove and apply properties of
rectangles.
Use properties of rectangles.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
rectangle : a quadrilateral with four right angles.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• A rectangle is just a special type of
parallelogram, so all the properties
of a parallelogram hold true:
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Consecutive angles are
supplementary
4. Diagonals bisect each other
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• However, because a rectangle is
made up of right triangles, there is
a 5 th property:
5. The diagonals are congruent.
A
B
E
D
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• Now, if the diagonals are congruent,
and they are bisected…what happens
when you cut two equal pieces of
string in half?
A
B
E
D
• So, what kind of triangles are inside a
rectangle?
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• Ex. Given that m 1 = 70, find the
measure of every other angle.
A
B
2
1
3
11
5 4 10
9E
D
6
7
8
12
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• Ex. Given that m 4 = 100, find the
measure of every other angle.
A
B
2
1
3
11
5 4 10
9E
D
6
7
8
12
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• Ex. Given m 8 = 3x and m 12 =
6x, find the value of x and the
measure of angles 8 and 12.
A
1
2
3
5 4 10
9E
11
B
D
6
7
8
12
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Example 1: Craft Application
A woodworker constructs a
rectangular picture frame so
that JK = 50 cm and JL = 86
cm. Find HM.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Lesson Quiz: Part I
A slab of concrete is poured with diagonal
spacers. In rectangle CNRT, CN = 35 ft, and
NT = 58 ft. Find each length.
1. TR 2. CE
Holt McDougal Geometry