unit 2 quadrilaterals. section 1 types of angles
TRANSCRIPT
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UNIT 2
QUADRILATE
RALS
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SECTION 1
TYPE
S OF
ANGLES
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NAME THE CONGRUENT ANGLES!• 1, 4, 5, 7
• 2, 3, 6, 8
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DIFFERENT TYPES OF ANGLES• Vertical angles: 1 and 4, directly
across from each other; always congruent
• Alternate interior angles: 3 and 6, inside the parallel lines on opposite sides of the transversal (form a “Z”)• Congruent when lines are parallel
• Corresponding angles: 1 and 5. in the same place at each intersection
• Consecutive angles: 3 and 5, inside the parallel lines on the same side• Supplementary when lines are parallel
• Supplementary = add up to 180°• Angles that form a line are also
supplementary, ( 1 and 2)
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FIND THE OTHER ANGLE MEASURES.
=120°
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ANGLES OF A POLYGON
• Interior angles of a polygon add up to 180(n – 2)• n is the number of sides
• Exterior angles of a polygon ALWAYS add up to 360°
Type of Polygon
nSum of Interior Angles
Measure of One Interior Angle
Sum of Exterior Angles
Measure of One
Exterior Angle
Triangle
Quadrilateral
3 180° 360°
4 360° 360°
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REGULAR POLYGONS• Regular polygon: polygon where all sides and angles are
congruent
• How do we find the measure of ONE angle on a regular polygon?• Divide the sum by the number of sides
• Interior angle:
• Exterior angle:
nn )2(180
n360
Type of Polygon
nSum of Interior Angles
Measure of One Interior Angle
Sum of Exterior Angles
Measure of One
Exterior Angle
Triangle 3 180° 360°60° 120°
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WRAP UP
• Exit Slip
• Unit 2 Homework Packet Due Friday
• Unit 2 Test Friday
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SECTION 2
PARALL
ELOGRAMS &
RHOMBUSES
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WHAT IS THIS CALLED?
PARALLELOGRAM!
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PROPERTIES OF A PARALLELOGRAM
• Opposite sides are parallel and congruent• •
• Opposite angles are congruent•
• Diagonals bisect each other• Bisect = to split in
half
CBADCDAB ,
CBADCDAB ,
CDAABCBCDDAB ,
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EXAMPLE 1
In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, AE = 2x + 8, and EC = 4x – 22. What is the value of x?
• What do AE and EC form?
• What do we know about the diagonals of a parallelogram?
• What do we now know about AE and EC?
• BONUS: Can you find the pairs of alternate interior angles and consecutive angles?
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EXAMPLE 2
In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, BE = ½x and ED = x – 4. What is the value of x?
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WRAP-UP
• Exit Slip
• Unit 2 Homework Packet
• Unit 2 Test
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SECTION 3
RECTANGLE
S, SQUARES, T
RAPEZOID
S
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SPECIAL QUADRILATERALS
Rhombus
Rectangle
SquareParallelogram
Quadrilateral
Trapezoid
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RHOMBUS
• A parallelogram with all four sides congruent
• Has all the properties of a parallelogram, plus:• 4 congruent sides• Diagonals are
perpendicular
• Food for thought : Are all rhombuses parallelograms? Are all parallelograms rhombuses?
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EXAMPLE 1
PQRS is a rhombus. PQ = 2/3x and SP = 2x – 12. Find x.
(Hint: Draw a sketch! You should always label the points of any figure in order.)
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RECTANGLE
• Parallelogram with four right angles
• Has all the properties of a parallelogram, plus:• Four right angles• Congruent diagonals
• Are all rectangles parallelograms? Are all parallelograms rectangles?
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EXAMPLE 2
Rectangle ABCD has angle ADB = 4x – 25 and angle DBC = x + 35. Find the measure of angle BDC.
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SQUARE
• Parallelogram with four congruent sides and four right angles
• Diagonals are congruent and perpendicular
• Combination of a rhombus and a rectangle
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EXAMPLE 3
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TRAPEZOID
• Quadrilateral with only ONE pair of opposite sides parallel
• Isosceles trapezoid• Legs (non-parallel sides)
are congruent• Base angles are
congruent• Diagonals are congruent
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EXAMPLE 4
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COMPARING QUADRILATERALS
ShapeFour Sides
Opposite Sides
Parallel
All Sides Congrue
nt
Four Right
Angles
Congruent
Diagonals
Perpendicular Diagonals
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square
Identify which shapes possess each property:
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WRAP UP
• Exit Slip
• Unit 2 Test Monday
• Unit 2 Homework Packet Due Monday