Bell Ringer Get out your notebook and prepare to take notes on
Chapter 7 List five shapes you see in the classroom
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7.1 - Pairs of Angles (Page 303) Essential Questions: 1. How do
we identify types of angles? 2. How can identifying types of angles
allow us to find relationships among angles?
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7.1 cont. Vertical angles Formed by two intersecting lines
Angles opposite one another are CONGRUENT Congruent - have the same
measure Adjacent angles Common vertex and common side
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7.1 cont. Example 1: Name a pair of adjacent angles and a pair
of vertical angles in the figure below: What is the measure of
angle HGK? 145
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7.1 cont. Supplementary angles Angles that add to 180 degrees
Complementary angles Angles that add to 90 degrees
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7.1 cont. Example 2: Find the measure of the supplement of the
angle IGJ in the following figure: What does the supplement you
found represent in the figure? 35
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7.1 cont. Perpendicular lines Two lines that intersect to form
a right angle
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7.1 cont. Example 3: In the following figure, if the measure of
angle DKH is 73, find the measures of the angles GKJ and JKF: 73 17
73
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7.1 - Closure 1. How do we identify types of angles? Vertical
angles, adjacent angles 2. How can identifying types of angles
allow us to find relationships among angles?
Complementary/supplementary angles Identify perpendicular
lines
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7.1 - Homework Page 305-306, 2-32 even
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Bell Ringer (7.2) Get out yesterdays homework assignment Get
out your notebook and prepare to take notes on Section 7.2 List two
sets of parallel lines you see in the classroom
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7.2 Angles and Parallel Lines (Page 307) Essential Questions:
1. What is a transversal? 2. What congruent angles are formed when
a transversal intersects two parallel lines?
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7.2 cont. Parallel Lines Equidistant at all points Transversal
A line that intersects two or more lines at different points
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7.2 cont. Corresponding Angles Lie on same side of the
transversal Have corresponding positions Are congruent ONLY when
lines are parallel Alternate Interior Angles Lie within a pair of
lines On opposite sides of the transversal Are congruent ONLY when
lines are parallel A E B F E HG F CD GH
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7.2 cont. Example 1: Identify each pair of corresponding angles
and each pair of alternate interior angles in the following
figure:
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7.2 cont. Example 2: If p is parallel to q in the following
figure, and the measure of angle 3 is 56, find the measure of angle
6. = 56
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7.2 cont. Example 3: In the figure below, explain how you know
? Alternate interior angles are congruent, therefore, lines a and b
are parallel.
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7.2 - Closure 1. What is a transversal? A line that intersects
two or more lines at different points 2. What congruent angles are
formed when a transversal intersects two parallel lines?
Corresponding angles Alternate interior angles
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7.2 - Homework Page 309-310, 2-28 even
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Bell Ringer (7.3) Get out yesterdays homework assignment Get
out your notebook and prepare to take notes on Section 7.3 List
five polygons you see in the classroom
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7.3 Congruent Polygons (Page 312) Essential Questions: 1. Which
parts of congruent figures can be congruent to each other? 2. What
are three ways we can demonstrate that two triangles are
congruent?
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7.3 cont. Congruent Polygons: Polygons that have the same size
and shape Can be slid, flipped, or turned so that one fits exactly
on top of the other Tick marks and arcs tell you which sides and
angles are congruent NOTE: When naming congruent polygons, list
corresponding vertices in the same order!! (i.e. ABC DEF)
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7.3 cont. Example 1: In the diagram below, list the congruent
parts of the two figures. Then write a congruence statement.
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7.3 cont. Showing Triangles are Congruent: Use corresponding
parts Use the following postulates: NOTE: Order of angles and sides
is important!!
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7.3 cont. Example 2: Show that the following pair of triangles
are congruent: Angle Side Angle by
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7.3 - Closure 1. Which parts of congruent figures can be
congruent to each other? Corresponding angles and sides 2. What are
three ways we can demonstrate that two triangles are congruent?
SSS, SAS, ASA
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7.3 - Homework Page 314-316, 2-28 even SKIP 22
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Bell Ringer (7.4) Get out yesterdays homework assignment Get
out your notebook and prepare to take notes on Section 7.4 Answer
the following question: What two characteristics do congruent
polygons have in common?
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7.4 Classifying Triangles and Quadrilaterals (Page 318)
Essential Question: How do we classify triangles and
quadrilaterals?
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7.4 cont. Classifying Triangles: Use angles and sides 6 types:
Acute (3 acute angles) Obtuse (1 obtuse angle) Right (1 right
angle) Equilateral (3 congruent sides) Isosceles (at least 2
congruent sides) Scalene (no congruent sides)
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7.4 cont. Example 1: Classify LMN by its sides and angles: 2
congruent sides 3 acute angles isosceles acute triangle
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7.4 cont. Classifying Quadrilaterals: Use angles and sides Name
quadrilaterals by listing vertices in consecutive order
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7.4 cont. Example 2: How would you classify the following
figure? Opposite sides are parallel Adjacent sides are not equal
Parallelogram
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7.4 - Closure How do we classify triangles and quadrilaterals?
Triangles angles or congruent sides Quadrilaterals sides and
angles
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7.4 - Homework Page 320, 2-18 even
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Bell Ringer Get out yesterdays homework assignment Think of any
clarifying questions you may have about 7.1-7.4 Draw and label a
trapezoid that contains a right angle.
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Mimio Software Match the angle pair with the proper name
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7.1-7.3 Review (Page 317)
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7.4 Review 1. Classify the following triangle according to its
angles and sides: 2. A triangles sides are all congruent and its
angles all measure 60. Classify the triangle. 3. Determine the best
name for the following quadrilateral: 4. What is the best name for
a figure that has four sides congruent, corresponding angles
parallel, and all four angles congruent?
7.5 cont. **Sum of the measures of the interior angles depends
on the number of sides in the polygon** Polygon Angle Sum: For a
polygon with n sides, the sum of the measures of the interior
angles is as follows:
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7.5 cont. Example 1: Find the sum of the measures of the
interior angles of an octagon. Octagon = 8 sides
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7.5 cont. Example 2: Find the missing angle measure in the
following hexagon: Hexagon = 6 sides = sum of angle measures
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7.5 cont. Regular Polygons: All sides and angles congruent
Equation for angle sum:
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7.5 cont. Example 3: A design tile is in the shape of a regular
nonagon. Find the measure of each angle. = 140
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7.5 - Closure How do we find the interior angle measures of a
polygon? For a polygon of n sides: For a regular polygon of n
sides:
Bell Ringer (7.6) Get out yesterdays homework assignment Get
out your notebook and prepare to take notes on Section 7.6 Find the
measure of each angle of a regular polygon with 14 sides. Round to
the nearest tenth. DO NOT LOSE THE FORMULA SHEET!!
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7.6 Areas of Polygons (Page 328) Essential Question: How do we
find the area of a parallelogram, triangle, and trapezoid?
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7.6 cont. Application: Construction Farming Architecture
Engineering Area: Number of square units a figure encloses
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7.6 cont.
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Example 1: Find the area of the following triangle:
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7.6 cont.
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Example 2: Find the area of the following parallelogram:
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7.6 cont.
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Example 3: Find the area of the following trapezoid:
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7.6 - Closure
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7.6 - Homework Page 331, 1-11, 15-17
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Bell Ringer (7.7) Get out yesterdays homework assignment Get
out your notebook and prepare to take notes on Section 7.7 Find the
area of the following trapezoid:
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7.7 Circumference and Area of a Circle (Page 336) Essential
Questions: How do we find the circumference and the area of a
circle? How can we use what we already know about area to find the
area of irregular figures?
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7.7 cont. Review: Radius Diameter Area
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7.7 cont.
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Example 1: Find the circumference and area of a circle with a
diameter of 9.2 inches. 9.2 in.
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7.7 cont. Example 2: Find the area of the following figure.
Round to the nearest tenth.
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7.7 - Closure
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7.7 - Homework Page 338-339 2-22 even, 26-30
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Bell Ringer
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7.1, 7.2 - Review (Page 346)
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7.3, 7.4 - Review (Page 347)
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7.5 - Review (Page 347)
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7.6, 7.7 - Review (Page 347)
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Flatland/Big Bang Theory Clips
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TEST TOMORROW!! Sections 7.1-7.7 Homework: Page 348, 1-29
Study: 7.1-7.7 Homework Notes Problems from todays review