Download Ch_ 6 Notes

Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
1
Warm-up:
Students Will Be Able To name polygons by side and angles.
6.1 Polygons
Polygon
3 or more segments called sides
Closed
o
No two sides intersect anywhere other
than the endpoints
o
All adjacent sides connect at the endpoints
Vertex
Connection of two segments at the endpoints
(corners)
# of sides
Name of polygon
Example
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
2
Convex
If each side was extended it would NOT pass
through the polygon
Nonconvex/
Concave
If any side is extended it will pass through the
polygon
Equilateral
All sides are congruent
Equiangular
All angles are congruent
Regular Polygon
Both equiangular and equilateral
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
3
Diagonal
Connects any two non-adjacent vertices of a
convex polygon
Interior Angles
of
Quadrilaterals
Theorem 6.1
The sum of the measures of the interior angles
of a quadrilateral equals _______________.
Homework:
6.1 worksheet
Warm-up:
Students Will Be Able To use properties of parallelograms to find unknown
measurements.
Properties of
Parallelograms
6.2 Parallelograms
Both pairs of opposite sides
are parallel
Opposite sides are congruent
(Theorem 6.2)
Opposite angles are congruent
(Theorem 6.3)
Adjacent angles are supplementary
(Theorem 6.4)
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
4
Diagonals bisect each other
(Theorem 6.5)
Examples:
FGHJ is a parallelogram. Find the unknown
lengths. Explain why.
a.
5
JH
3
b.
HK
PQRS is a parallelogram. Find the angle
measure.
m∠R
a.
b.
m∠Q
70o
PQRS is a parallelogram. Find the value of x.
3xo
120o
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
5
Given:
ABCD is a parallelogram
Prove:
AB ≅ CD , AD ≅ CB
1.
Statement
1.
2.
2.
4.
4.
3.
Reason
3.
5.
5.
6.
6.
7.
Homework:
7.
6.2 worksheet
Warm-up:
Students Will Be Able To use prove quadrilateral to be parallelograms.
6.3 Proving Quadrilaterals are Parallelograms
Proof of
Parallelograms
Opposite sides are congruent
(Theorem 6.7)
Opposite angles are congruent
(Theorem 6.8)
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
6
If an angle of a quadrilateral is
supplementary to both of its
consecutive angles, then the
quadrilateral is a parallelogram
(Theorem 6.9)
Diagonals bisect each other
(Theorem 6.9)
Given:
Prove:
AB ≅ CD , AD ≅ CB
ABCD is a parallelogram
Statement
1.
Reason
1.
2.
2.
4.
4.
3.
5.
6.
Examples:
3.
5.
6.
Describe how you would prove that ABCD is a
parallelogram.
1.
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
7
2.
Homework:
Warm-up:
6.3 worksheet
Quiz 6.1-6.3
Warm-up:
Students Will Be Able To use prove determine what type of quadrilateral
using properties of quadrilaterals.
6.4 Rhombuses, Rectangles, and Squares
Rectangle
Opposite sides parallel
Opposite sides congruent
All angles congruent
Diagonals are congruent (Theorem 6.13)
Diagonals bisect each other
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
8
Rhombus
Opposite sides parallel
All sides congruent
Opposite angles congruent
Adjacent angles supplementary
Diagonals bisect each other
Diagonals are perpendicular (Theorem 6.11)
Diagonals bisect a pair of opposite angles
(Theorem 6.12)
Square
Opposite sides are parallel
All sides congruent
All angles congruent
Diagonals bisect each other
Diagonals are perpendicular
Diagonals bisect a pair of opposite angles
Diagonals are congruent
Examples:
Find the value of x.
1.
Rectangle
8
6
2.
Rhombus
32o
x
4xo
Homework:
6.4 worksheet
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
9
Warm-up:
Students Will Be Able To use the properties of quadrilateral to determine
exactly which type of quadrilateral it is.
6.5 Trapezoids and Kites
Trapezoid
Two bases are parallel
Two legs that connect the parallel sides
Base angles on opposite sides of the same leg are
supplementary
Isosceles
Trapezoid
Legs are congruent
If a trapezoid is isosceles, then each pair of base
angles is congruent (Theorem 6.14)
If a trapezoid has a pair of congruent base
angles, then it is an isosceles trapezoid (Theorem
6.15)
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
10
Isosceles
Trapezoid
A trapezoid is isosceles if and only if its diagonals
are congruent (Theorem 6.16)
Midsegment
Theorem for
Trapezoids
The midsegment of a trapezoid is parallel to each
base and its length is one half the sum of the
lengths of the bases (Theorem 6.17)
Kite
Adjacent sides congruent
One pair of opposite angles congruent
Diagonals are perpendicular
Diagonals bisect one set of opposite angles
Find the length of the midsegment.
12
1.
18
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
11
2.
9
17
Homework:
6.5 worksheet
Warm-up:
Students Will Be Able To use the properties of quadrilateral to determine
exactly which type of quadrilateral it is.
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
12
6.6 Special Quadrilaterals
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Quadrilaterals hold all the properties of the figures above them.
Name _________________________________________________________ Hour __________
Ch. 6 Quadrilaterals
Geometry
13
Examples:
Homework:
Warm-up:
Identify the special quadrilateral. Use the most
specific name.
1.
2.
6.6 worksheet
Quiz 6.4-6.6
Warm-up:
Homework:
Ch. 6 Review Wkst.
Name _________________________________________________________ Hour __________
Warm-up:
Homework:
Ch. 6 Review Wkst.
Warm-up:
Ch. 6 Test
14