Transcript Unit 2 - mszhu

NAME THE CONGRUENT ANGLES!
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1, 4, 5, 7
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2, 3, 6, 8
DIFFERENT TYPES OF ANGLES
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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
place at each intersection
5. in the same
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)
FIND THE OTHER ANGLE MEASURES.
=120°
ANGLES OF A POLYGON
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Interior angles of a polygon add up to 180(n – 2)
• n is the number of sides
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Exterior angles of a polygon ALWAYS add up to 360°
n
Sum of
Interior
Angles
Triangle
3
180°
360°
Quadrilateral
4
360°
360°
Type of
Polygon
Measure of
One Interior
Angle
Sum of
Exterior
Angles
Measure of
One Exterior
Angle
REGULAR POLYGONS
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Regular polygon: polygon where all sides and angles are congruent
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How do we find the measure of ONE angle on a regular polygon?
• Divide the sum by the number of sides
Type of
Polygon
Triangle
• Interior angle:
180(n  2)
n
• Exterior angle:
360
n
n
Sum of
Interior
Angles
Measure of
One Interior
Angle
Sum of
Exterior
Angles
3
180°
60°
360°
Measure of
One Exterior
Angle
120°
WRAP UP
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Exit Slip
•
Unit 2 Homework Packet Due Friday
•
Unit 2 Test Friday
WHAT IS THIS CALLED?
PARALLELOGRAM!
PROPERTIES OF A PARALLELOGRAM
• Opposite sides are
parallel and congruent
• AB  CD, AD  CB
• AB CD, AD CB
• Opposite angles are
congruent
•DAB  BCD, ABC  CDA
• Diagonals bisect each
other
• Bisect = to split in half
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?
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?
WRAP-UP
• Exit Slip
• Unit 2 Homework Packet
• Unit 2 Test
SPECIAL QUADRILATERALS
Trapezoid
Quadrilateral
Rhombus
Square
Parallelogram
Rectangle
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?
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.)
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?
EXAMPLE 2
Rectangle ABCD has angle ADB = 4x – 25 and angle DBC = x + 35.
Find the measure of angle BDC.
SQUARE
• Parallelogram with four congruent
sides and four right angles
• Diagonals are congruent and
perpendicular
• Combination of a rhombus and a
rectangle
EXAMPLE 3
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
EXAMPLE 4
COMPARING QUADRILATERALS
Identify which shapes possess each property:
Shape
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square
Four
Sides
Opposite
Sides
Parallel
All Sides
Congruent
Four
Right
Angles
Congruent Perpendicular
Diagonals
Diagonals
WRAP UP
• Exit Slip
• Unit 2 Test Monday
• Unit 2 Homework Packet Due Monday