6-4 Properties of Special Parallelograms Properties of Special ...

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

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

6-4 Properties of Special Parallelograms
rhombus : a quadrilateral with four congruent
sides.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Like a rectangle, a rhombus is a parallelogram. So you
can apply the properties of parallelograms to
rhombuses.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• Special Properties of a Rhombus:
1. Diagonals are perpendicular:
2. Diagonals bisect the opposite angles:
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• This means that just like a rectangle, if I
know one angle of a rhombus, I can find
all the others.
• Ex. Given m
angles.
8
1 = 32, find all the other
12 11
10
9
7 6
5 4 3
2
1
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
• If the diagonals are perpendicular, then
that means we have four right triangles.
This means we can use the Pythagorean
Theorem!
• Ex. Given AC = 24 cm and BD = 10 cm,
Afind the perimeter B of the rhombus.
D
C
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Example 2A: Using Properties of Rhombuses to Find
Measures
TVWX is a rhombus.
Find TV.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Example 2B: Using Properties of Rhombuses to Find
Measures
TVWX is a rhombus.
Find a.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Square : a quadrilateral with four right angles and
four congruent sides. A square is a parallelogram, a
rectangle, and a rhombus. So a square has the
properties of all three.
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
1. Diagonals are congruent – so split
in four equal parts.
2. Diagonals are perpendicular – so
makes right triangles
3. Diagonals bisect opposite angles.
2
1
9
10
Holt McDougal Geometry
3
4
7 6 5
8
12
11

6-4 Properties of Special Parallelograms
• Use the last two properties to find all
the angles of the square.
2
1
9
10
3
4
7 6 5
8
12
11
Holt McDougal Geometry

6-4 Properties of Special Parallelograms
Lesson Quiz: Part II
PQRS is a rhombus. Find each measure.
3. QP 4. m QRP
Holt McDougal Geometry