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Lesson 6-2

Lesson 6-2. Parallelograms. 8x+12 °. 5-Minute Check on Lesson 6-1. Find the measure of an interior angle given the number of sides of a regular polygon . 10 2. 12 Find the measure of the sums of the interior angles of each convex polygon

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Lesson 6-2

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  1. Lesson 6-2 Parallelograms

  2. 8x+12° 5-Minute Check on Lesson 6-1 • Find the measure of an interior angle given the number of sides of a regular polygon. • 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. What is the measure of an interior angle of a regular hexagon? Standardized Test Practice: A B C D 135 90 108 120 Click the mouse button or press the Space Bar to display the answers.

  3. 8x+12° 5-Minute Check on Lesson 6-1 • Find the measure of an interior angle given the number of sides of a regular polygon. • 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. What is the measure of an interior angle of a regular hexagon? 150 144 3240 2520 8x + 12 = 108 8x = 96 x = 12 Standardized Test Practice: A B C D 135 90 108 120 Click the mouse button or press the Space Bar to display the answers.

  4. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites Trapezoids IsoscelesTrapezoids 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 A B Parallelogram CharacteristicsOpposite Sides Parallel and Congruent Opposite Angles Congruent Consecutive ’s Supplementary C D A B Diagonal CharacteristicsBisect 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. If lines are cut by a transversal, alt. int. Example 2-2a RSTU is a parallelogram. Find mURT , mSRT and y. Definition of congruent angles Substitution Angle Addition Theorem

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

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

  11. MULTIPLE-CHOICE TEST ITEMWhat 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)? Find the midpoint of Midpoint Formula A B C D Read the Test ItemSince the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of Example 2-3a Solve the Test Item Answer: C

  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 basesMedian = ½ (base + base) Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangles Rhombi IsoscelesTrapezoids 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: • 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 403-05; 2-5, 15-17, 31-36

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