1. Lesson 8-2
Parallelograms

2. 5-Minute Check on Lesson 8-1
Transparency 8-2
5-Minute Check on Lesson 8-1
Find the measure of an interior angle given the number of sides of a regular polygon.
Find the measure of the sums of the interior angles of each convex polygon
gon gon
5. Find x, if QRSTU is a regular pentagon
What is the measure of an interior angle of a regular hexagon?
8x+12°
Standardized Test Practice: A 90 B
108 C
120 D
135
Click the mouse button or press the Space Bar to display the answers.

3. 5-Minute Check on Lesson 8-1
Transparency 8-2
5-Minute Check on Lesson 8-1
Find the measure of an interior angle given the number of sides of a regular polygon.
Find the measure of the sums of the interior angles of each convex polygon
gon gon
5. Find x, if QRSTU is a regular pentagon
What is the measure of an interior angle of a regular hexagon?
144
150
3240
2520
8x+12°
8x + 12 = x = x = 12
Standardized Test Practice: A 90 B
108 C
120 D
135
Click the mouse button or press the Space Bar to display the answers.

4. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites
Trapezoids
Isosceles Trapezoids
Rectangles
Rhombi
Squares

5. 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

6. Vocabulary
Parallelogram – a quadrilateral with parallel opposite sides

7. Parallelograms Parallelogram Characteristics Opposite Sides ParallelB
Parallelogram Characteristics Opposite Sides Parallel
and Congruent
Opposite Angles Congruent
Consecutive ’s Supplementary C D A 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 (for example ∆ADC  ∆DAB) M C D

8. 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
Example 2-2a

9. Subtract 58 from each side.
Substitution
Subtract 58 from each side.
Definition of congruent segments
Substitution
Divide each side by 3.
Answer:
Example 2-2b

10. ABCD is a parallelogram. Find mBDC, mBCD and x.
Answer:
Example 2-2d

11. A B C D
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)?
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
Example 2-3a

12. Quadrilateral Characteristics Summary
Convex Quadrilaterals
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Parallelograms
Trapezoids
Bases Parallel
Legs are not Parallel
Leg angles are supplementary
Median is parallel to bases Median = ½ (base + base)
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Rhombi
Isosceles Trapezoids
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Angles all 90°
Diagonals congruent
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Squares
Diagonals divide into 4 congruent triangles

13. Summary & Homework Summary: Homework:
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 ; 16, 19-24, 29-31, 46