int math 2 section 5-6 1011
DESCRIPTION
Quadrilaterals and ParallelogramsTRANSCRIPT
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SECTION 5-6Quadrilaterals and Parallelograms
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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
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VOCABULARY
1. Quadrilateral:
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:
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VOCABULARY
1. Quadrilateral: A four-sided figure
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:
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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:
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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:
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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:
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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:
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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
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QUADRILATERAL HIERARCHY
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QUADRILATERAL HIERARCHY
Quadrilateral
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
Rectangle
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
4 equalsides
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QUADRILATERAL HIERARCHY
Quadrilateral4 sides
Trapezoid1 pair parallel
sides
Parallelogram
2 pairs parallelsides
RectangleOpposite sides
congruent,90° angles
Rhombus
4 equalsides
Square
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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
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PROPERTIES OF PARALLELOGRAMS
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PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
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PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
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PROPERTIES OF PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
3.Consecutive angles are supplementary
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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°
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DIAGONALS OF PARALLELOGRAMS
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DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
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DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
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DIAGONALS OF PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
7.Diagonals of a rhombus are perpendicular
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EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
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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
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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
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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
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EXAMPLE 1
a. If AE = 5x - 3 and EC = 15 - x, find AC.
In parallelogram ABCD, diagonals AC and BD intersect at E.
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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.
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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.
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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.
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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.
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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.
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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
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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
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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.
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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.
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EXAMPLE 1
b. If DE = 4y + 1 and EB = 5y - 1, find DB.
In parallelogram ABCD, diagonals AC and BD intersect at E.
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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.
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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.
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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.
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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.
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EXAMPLE 2
b. In rectangle ABCD, diagonals AC and BD intersect at E.
Which pair of triangles is not congruent? Draw a picture first.
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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
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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.
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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
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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
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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
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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
![Page 66: Int Math 2 Section 5-6 1011](https://reader036.vdocuments.site/reader036/viewer/2022062405/55850515d8b42ae71b8b520e/html5/thumbnails/66.jpg)
PROBLEM SET
Mon, Jan 31
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PROBLEM SET
p. 218 #1-43 odd
“Make visible what, without you, might perhaps never have
been seen.” - Robert Bresson
Mon, Jan 31