int math 2 section 5-6 1011
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Quadrilaterals and ParallelogramsTRANSCRIPT
SECTION 5-6Quadrilaterals and Parallelograms
Mon, Jan 31
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
Mon, Jan 31
VOCABULARY
1. Quadrilateral:
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:
Mon, Jan 31
VOCABULARY
1. Quadrilateral: A four-sided figure
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:
Mon, Jan 31
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:
Mon, Jan 31
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:
Mon, Jan 31
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:
Mon, Jan 31
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:
Mon, Jan 31
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
Mon, Jan 31
QUADRILATERAL HIERARCHY
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
Rectangle
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
4 equalsides
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
4 equalsides
Square
Mon, Jan 31
QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
4 equalsides
Square4 equal sides4 90° angles
Mon, Jan 31
PROPERTIES OF PARALLELOGRAMS
Mon, Jan 31
PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
Mon, Jan 31
PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
Mon, Jan 31
PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
3.Consecutive angles are supplementary
Mon, Jan 31
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°
Mon, Jan 31
DIAGONALS OF PARALLELOGRAMS
Mon, Jan 31
DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
Mon, Jan 31
DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
Mon, Jan 31
DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
7.Diagonals of a rhombus are perpendicular
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC =
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3 = 12
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3 = 12
AC = AE + EC
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3 = 12
AC = AE + EC
AC = 12+ 12
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3 = 12
AC = AE + EC
AC = 12+ 12
AC = 24
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
6 6 x = 3
AE = EC = 15−3 = 12
AC = AE + EC
AC = 12+ 12
AC = 24 units
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
4y + 1 = 5y − 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
4y + 1 = 5y − 1 −4y −4y +1 +1
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 = 9 4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 = 9
DB = DE + EB 4y + 1 = 5y − 1
−4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 = 9
DB = DE + EB
DB = 9+9
4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 = 9
DB = DE + EB
DB = 9+9
DB = 18
4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
DE = EB = 4(2)+ 1 = 9
DB = DE + EB
DB = 9+9
DB = 18 units
4y + 1 = 5y − 1 −4y −4y +1 +1
2 = y
In parallelogram ABCD, diagonals AC and BD intersect at E.
Mon, Jan 31
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.
Mon, Jan 31
EXAMPLE 2
Discuss on edmodo, have an answer for class tomorrow
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.
Mon, Jan 31
EXAMPLE 2
b. In rectangle ABCD, diagonals AC and BD intersect at E.
Which pair of triangles is not congruent? Draw a picture first.
Mon, Jan 31
EXAMPLE 2
b. In rectangle ABCD, diagonals AC and BD intersect at E.
Which pair of triangles is not congruent? Draw a picture first.
Discuss on edmodo, have an answer for class tomorrow
Mon, Jan 31
EXAMPLE 2
a. XZ b. m∠YXZ
c. m∠XYW d. ZW
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.
Mon, Jan 31
EXAMPLE 2
a. XZ b. m∠YXZ
c. m∠XYW d. ZW
21.5 in.
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.
Mon, Jan 31
EXAMPLE 2
a. XZ b. m∠YXZ
c. m∠XYW d. ZW
21.5 in. 135°
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.
Mon, Jan 31
EXAMPLE 2
a. XZ b. m∠YXZ
c. m∠XYW d. ZW
21.5 in. 135°
45°
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.
Mon, Jan 31
EXAMPLE 2
a. XZ b. m∠YXZ
c. m∠XYW d. ZW
21.5 in. 135°
45° Not enough info
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.
Mon, Jan 31
PROBLEM SET
Mon, Jan 31
PROBLEM SET
p. 218 #1-43 odd
“Make visible what, without you, might perhaps never have
been seen.” - Robert Bresson
Mon, Jan 31