Integrated Math 2 Section 5-6
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Integrated Math 2 Section 5-6

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Quadrilaterals and Parallelograms

Quadrilaterals and Parallelograms

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Integrated Math 2 Section 5-6 Integrated Math 2 Section 5-6 Presentation Transcript

  • SECTION 5-6 Quadrilaterals and Parallelograms
  • ESSENTIAL QUESTIONS How do you classify different types of quadrilaterals? What are the properties of parallelograms, and how do you use them? Where you’ll see this: Construction, civil engineering, navigation
  • VOCABULARY 1. Quadrilateral: 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides:
  • VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides: Sides in a quadrilateral that do touch each other
  • QUADRILATERAL HIERARCHY
  • QUADRILATERAL HIERARCHY Quadrilateral
  • QUADRILATERAL HIERARCHY Quadrilateral 4 sides
  • QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid
  • QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 4 sides Trapezoid 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Trapezoid 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Trapezoid 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides Square
  • QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides Square 4 equal sides 4 90° angles
  • PROPERTIES OF PARALLELOGRAMS
  • PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent
  • PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent
  • PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary
  • PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary 4.The sum of the angles is 360°
  • DIAGONALS OF PARALLELOGRAMS
  • DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other
  • DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent
  • DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent 7. Diagonals of a rhombus are perpendicular
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 6 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 6 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 6 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24 units
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB.
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1 2=y
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = −4y +1 −4y +1 2=y
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 −4y +1 −4y +1 2=y
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 2=y
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18
  • EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18 units
  • EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first.
  • EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first. Class poll and discussion
  • EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first.
  • EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first. Class poll and discussion
  • EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ c. m∠XYW d. ZW
  • EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. c. m∠XYW d. ZW
  • EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW
  • EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45°
  • EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45° Not enough info
  • HOMEWORK
  • HOMEWORK p. 218 #1-43 odd “Make visible what, without you, might perhaps never have been seen.” - Robert Bresson