Transcript Document

Lesson 8-2
Parallelograms
5-Minute Check on Lesson 8-1
Transparency 8-2
Find the measure of an interior angle given the number of sides of a
regular polygon.
1. 10
2. 12
Find the measure of the sums of the interior angles of each convex
polygon
3. 20-gon
4. 16-gon
5. Find x, if QRSTU is a regular pentagon
6.
Standardized Test Practice:
What is the measure of an interior angle of a
regular hexagon?
A
90
B
108
C
8x+12°
120
D
135
Click the mouse button or press the
Space Bar to display the answers.
5-Minute Check on Lesson 8-1
Transparency 8-2
Find the measure of an interior angle given the number of sides of a
regular polygon.
1. 10
2. 12
144
150
Find the measure of the sums of the interior angles of each convex
polygon
3. 20-gon
4. 16-gon
3240
2520
5. Find x, if QRSTU is a regular pentagon
8x + 12 = 108
6.
8x = 96
Standardized Test Practice:
x = 12
What is the measure of an interior angle of a
regular hexagon?
A
90
B
108
C
8x+12°
120
D
135
Click the mouse button or press the
Space Bar to display the answers.
Polygon Hierarchy
Polygons
Quadrilaterals
Parallelograms
Rectangles
Rhombi
Squares
Kites
Trapezoids
Isosceles
Trapezoids
Objectives
• Recognize and apply properties of the sides
and angles of parallelograms
– Opposite sides equal
– Opposite angles equal
– Consecutive angles supplementary
• Recognize and apply properties of the
diagonals of parallelograms
– Diagonals bisect each other
Vocabulary
• Parallelogram – a quadrilateral with parallel
opposite sides
Parallelograms
A
B
Parallelogram Characteristics
Opposite Sides Parallel
and Congruent
Opposite Angles Congruent
Consecutive ’s Supplementary
C
A
D
B
Diagonal Characteristics
Bisect each other (AM=DM, CM=BM)
Not necessarily equal length (AD ≠ BC)
Share a common midpoint (M)
Separates into two congruent ∆’s
M
C
D
(for example ∆ADC  ∆DAB)
RSTU is a parallelogram. Find mURT , mSRT and y.
If lines are cut by a transversal,
alt. int.
Definition of congruent angles
Substitution
Angle Addition Theorem
Substitution
Subtract 58 from each
side.
Definition of congruent segments
Substitution
Divide each side by 3.
Answer:
ABCD is a parallelogram. Find mBDC, mBCD and x.
Answer:
MULTIPLE-CHOICE TEST ITEM
What are the coordinates of the intersection of the
diagonals of parallelogram MNPR, with vertices
M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
A
B
C
D
Read the Test Item
Since the diagonals of a parallelogram bisect each other,
the intersection point is the midpoint of
Solve the Test Item
Find the midpoint of
Midpoint Formula
Answer: C
Quadrilateral Characteristics Summary
Convex Quadrilaterals
Parallelograms
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Trapezoids
Bases Parallel
Legs are not Parallel
Leg angles are supplementary
Median is parallel to bases
Median = ½ (base + base)
Rhombi
Angles all 90°
Diagonals congruent
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Squares
Diagonals divide into 4 congruent triangles
Isosceles
Trapezoids
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Summary & Homework
• Summary:
– In a parallelogram, opposite sides are parallel and
congruent, opposite angles are congruent, and
consecutive angles are supplementary
– Diagonals of a parallelogram bisect each other.
• Homework:
– pg 415-416; 16, 19-24, 29-31, 46