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Geometry 2206
Unit 3:
Mrs. Bondi
Unit 3: Two-Dimensional Shapes
Lesson Topics:
Lesson 1: Congruent Figures (PH text 4.1)
Lesson 2: Triangle Congruence by SSS and SAS (PH text 4.2)
Lesson 3: Triangle Congruence by ASA and AAS (PH text 4.3)
Lesson 4: Using Corresponding Parts of Congruent Triangles (PH text 4.4)
Lesson 5: Isosceles and Equilateral Triangles (PH text 4.5)
Lesson 6: Congruence in Right Triangles (PH text 4.6)
Lesson 7: Congruence in Overlapping Triangles (PH text 4.7)
Lesson 8: Midsegments of Triangles (PH text 5.1)
Lesson 9: Perpendicular and Angle Bisectors (PH text 5.2)
Lesson 10: Bisectors in Triangles (PH text 5.3)
Lesson 11: Medians and Altitudes (PH text 5.4)
Lesson 12: Indirect Proof (PH text 5.5)
Lesson 13: Inequalities in One Triangle (PH text 5.6)
Lesson 14: Inequalities in Two Triangles (PH text 5.7)
Lesson 15: The Polygon-Angle Sum Theorems (PH text 6.1)
Lesson 16: Properties of Parallelograms (PH text 6.2)
Lesson 17: Proving that a Quadrilateral is a Parallelogram (PH text 6.3)
Lesson 18: Properties of Rhombuses, Rectangles, and Squares (PH text 6.4)
Lesson 19: Conditions for Rhombuses, Rectangles, and Squares (PH text 6.5)
Lesson 20: Trapezoids and Kites (PH text 6.6)
Lesson 21: Polygons in the Coordinate Plane (PH text 6.7)
Lesson 22: Applying Coordinate Geometry (PH text 6.8)
Lesson 23: Proofs Using Coordinate Geometry (PH 6.9)
Lesson 24: Proportions in Triangles (PH text 7.5)
Lesson 25: Areas of Parallelograms and Triangles (PH text 10.1)
Lesson 26: Areas of Trapezoids, Rhombuses and Kites (PH text 10.2)
Lesson 27: Areas of Regular Polygons (PH text 10.3)
Lesson 28: Perimeters and Areas of Similar Figures (PH text 10.4)
Lesson 29: Trigonometry and Area (PH text 10.5)
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 15: The Polygon-Angle Sum (PH text 6.1)
Objective:
to find the sum of the both interior and exterior angles of a polygon
Theorem 6-1
Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is __________________
Example 1: If m∠B = m∠D, find m∠B in ABCD.
B
A
100°
40°
D
Equiangular Polygon
C
Equilateral Polygon
Regular Polygon
Corollary to Polygon Interior Angle-Sum Theorem
The measure each interior angle of a regular n-gon is __________________
Example 2: What is the measure each interior angle of a regular nonagon?
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Geometry 2206
Unit 3:
Theorem 6-2
Mrs. Bondi
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is ________
Example 3: Find the measure of each interior angle. What is the sum of the interior angles?
Extend one side at each vertex and find the exterior angle that was formed. What is the sum of
the exterior angles?
Check out this explanation. http://www.mathsisfun.com/geometry/exterior-angles-polygons.html
Example 4: Find the measure of an interior and an exterior angle of a regular pentagon.
Practice:
HW: p.356 #6-36 even
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 16: Properties of Parallelograms (PH text 6.2)
Objective:
to find relationships among angles, sides, and diagonals of parallelograms
Parallelogram:
Theorem 6-3
Opposite sides of a parallelogram are congruent.
Prove the theorem.
Given:
ABCD
Prove:
AB  CD
BC  DA
B
A
Statement
C
D
Reason
Consecutive Angles:
Theorem 6-4
Theorem 6-5
Consecutive angles of a parallelogram are supplementary.
Opposite angles of a parallelogram are congruent.
A
4
B
C
A
D
B
C
D
Geometry 2206
Unit 3:
Theorem 6-6
Mrs. Bondi
The diagonals of a parallelogram bisect each other.
B
C
A
Theorem 6-7
D
If three (or more) parallel lines cut off congruent segments on one transversal,
then they cut off congruent segments on every transversal.
If AB CD EF and AC  CE , then BD  DF .
A
C
E
(Try dividing an index card into four congruent vertical sections using notebook paper.)
Practice:
HW: p.364 #9-40, 43 (at least 4 proofs)
5
B
D
F
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 17: Proving that a Quadrilateral is a Parallelogram (PH text 6.3)
Objective:
Theorem 6-8
Prove it:
Given:
Prove:
to determine whether a quadrilateral is a parallelogram
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
B
AB  CD
BC  DA
ABCD is a
C
A
Statement
D
Reason
Theorem 6-9
If an angle of a quadrilateral is supplementary
to both of its consecutive angles, then the
quadrilateral is a parallelogram.
Theorem 6-10
If both pairs of opposite angles of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.
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Geometry 2206
Unit 3:
Mrs. Bondi
Example 1: Find the value of each variable to make the figure a parallelogram.
Theorem 6-11
Prove it:
Given:
Prove:
If the diagonals of a quadrilateral
bisect each other, then the
quadrilateral is a parallelogram.
B
AC and BD bisect
each other at E
ABCD is a parallelogram
A
Statement
Theorem 6-12
D
Reason
If one pair of opposite sides of a
quadrilateral is both congruent and
parallel, then the quadrilateral is a
parallelogram.
7
C
Geometry 2206
Unit 3:
Mrs. Bondi
Is it possible to prove that the quadrilateral is a parallelogram based on the given information? Explain.
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Geometry 2206
Unit 3:
Mrs. Bondi
Practice:
HW: p.372 # 6-24 + two additional proofs
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 18: Properties of Rhombuses, Rectangles, and Squares (PH text 6.4, 6.6)
Objectives:
to define and classify special types of parallelograms.
to use properties of diagonals of rhombuses and rectangles
Special Quadrilaterals:
Parallelogram:
Example:
Rhombus:
Rectangle:
Example:
Example:
Square:
Kite:
Example:
Example:
Trapezoid:
Isosceles Trapezoid:
Example:
Example:
Example 1: Judging by appearance, name the quadrilateral in as many ways as possible.
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Geometry 2206
Unit 3:
Mrs. Bondi
Example 2: Given C(1, 2), D(5, 2), E(7,-2), F(-1, -2), determine the
most precise name for quadrilateral CDEF.
Theorem 6-13
Prove it:
Given:
Prove:
The diagonals of a rhombus are perpendicular.
Rhombus ABCD
AC  BD
B
C
A
Statement
D
Reason
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Geometry 2206
Unit 3:
Theorem 6-14
Prove it:
Given:
Prove:
Mrs. Bondi
Each diagonal of a rhombus bisects
the two opposite angles.
Rhombus ABCD
1  2
3  4
B
C
1
A
2
Statement
3
4
D
Reason
Example 3: If mABC = 120, find the measures of the numbered angles.
B
Rhombus ABCD
C
5
1
A
12
2
3
4
D
Geometry 2206
Unit 3:
Mrs. Bondi
Theorem 6-15
The diagonals of a rectangle are congruent.
Prove it:
Given:
Prove:
Rectangle ABCD
AC  DB
Statement
B
C
A
D
Reason
Practice:
HW: p.379 # 6-44 even, 50-56 even
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 19: Conditions for Rhombuses, Rectangles, and Squares (PH text 6.5)
Objectives:
Theorem 6-16
Prove it:
Given:
Prove:
to determine whether a parallelogram is a rhombus or a rectangle.
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a
rhombus.
ABCD and AC  BD
ABCD is a rhombus
B
A
Statement
C
D
Reason
Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the
parallelogram is a rhombus.
Theorem 6-18
If the diagonals of a parallelogram are congruent, then the parallelogram is a
rectangle.
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Geometry 2206
Unit 3:
Mrs. Bondi
Examples: Use the given information to identify each quadrilateral with any names that work
for it. Also identify its most specific name. (It is often helpful to draw a sketch.)
1. a diagonal bisects two angles
2. the diagonals are congruent
3. the diagonals bisect each other
4. the angle measures are 35, 145, 35, 145
5. the diagonals are perpendicular
Example 6: For what values of x is
B
C
3x
7x - 2
A
ABCD a rhombus?
D
Example 7: For what values of x is
B
ABCD a rectangle?
C
7x - 2
A
5x - 8
D
Practice:
HW: p.386 #6-19, 23-24, 32-34
15
(The expressions are labeling the pieces of the diagonals.)
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 20: Trapezoids and Kites (PH text 6.6)
Objective:
bases
to verify and use properties of trapezoids and kites
base angles
trapezoid –
isosceles trapezoid –
Theorem 6-19
Example 1:
legs
Base angles of an isosceles trapezoid are congruent.
15
Find the height of the trapezoid.
13
13
25
Example 2: A circular dart board has 20 sections meeting in the middle.
What are the base angles of the trapezoids formed in the second ring?
Theorem 6-20
Prove it:
Given:
Prove:
The diagonals of an isosceles trapezoid
are congruent.
B
Isosceles Trapezoid ABCD
with AB  DC
AC  DB
C
A
Statement
D
Reason
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Geometry 2206
Unit 3:
Mrs. Bondi
Midsegment of a trapezoid –
Theorem 6-21
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to its bases AND the length of the
midsegment is half the sum of the lengths of the bases
Example 2:
x+3
For what values of x can we call this a midsegment?.
2x - 4
24
kite –
Theorem 6-22
Prove it:
Given:
Prove:
The diagonals of a kite are perpendicular.
R
Kite RSTW with
RS  RW and ST  WT
RT  SW
W
Statement
S
Reason
T
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Geometry 2206
Unit 3:
Mrs. Bondi
R
Problem: Given Kite RSTW, find the value of RT.
RS = 13 cm
ST = 15 cm
SW = 24 cm
RT = ?
W
S
T
Example 3: Refer to the kite diagram below. If KT  x  4 , KB  2x  4 , JB  y  4 , and JT  2 x ,
find the values of x and y.
T
J
K
B
Quadrilateral Summary:
(include 8 types of figures)
Practice:
HW: p.394 #8-70 even (do at least two of the proofs)
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Geometry 2206
Unit 3:
Mrs. Bondi
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Geometry 2206
Unit 3:
Mrs. Bondi
Mid-Chapter Quiz – p.398
Prepare for a quiz!
Algebra Review – Simplifying Radicals – p.399
Be sure you remember these skills!
More Radical Practice:
1. A pool is shaped like a rectangle with a length 4 times its width w. What is an expression for the
distance between opposite corners of the pool?
2. Evelyn rode her horse along a triangular path. The distance she traveled south was five times the
distance she traveled east. Then she rode directly back to her starting point. What is an expression for
the total distance she rode?
3. You are making a mosaic design on a square table top. You have already covered half of the
table top with 150 1-inch square tile pieces.
a. What are the dimensions of the table top?
b. What is the measure of the diagonal from one corner to the opposite corner of the table top?
4. The equation r 
SA
gives the radius r of a sphere with surface area SA. What is the radius of a
4
sphere with the given surface area? Use 3.14 for π.
a. 1256 in2.
b. 200.96 cm 2
c. 379.94 ft2
6. Open-Ended What are three radical expressions that simplify to 2 x 3 ?
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Geometry 2206
Unit 3:
Mrs. Bondi
Algebra Review:
21
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 21: Polygons in the Coordinate Plane (PH text 6.7)
Objective:
to classify polygons in the coordinate plane
Reminder:
In Coordinate Geometry, we combine our knowledge of geometry and algebra to
identify shapes, find missing vertices, or prove shape characteristics. This is useful for
many real-world applications.
Examples:
1)
Name the type of triangle is formed by
A (2, 0), B (3, 4), C (-1 , 1)
Use the distance formula to find length of:
AB
BC
CA
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Geometry 2206
Unit 3:
Mrs. Bondi
2) Prove
EFGH is a parallelogram.
E (-5, -3), F (-2, 6), G (2 , 7), H (-1 , -2)
Use the slope formula to find slope of:
EF
FG
GH
HE
3)
Give the most precise name for JKLM .
J (-2, 4), K (2, 2), L (4 , -2), M (-4 , -4)
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Geometry 2206
Unit 3:
Mrs. Bondi
A quadrilateral formed by joining the midpoints of the sides of any quadrilateral will be
a parallelogram.
4)
Plot the vertices of kite ABCD. What is the shape of the
quadrilateral formed by the midpoints?
A (-2, 4), B (2, 2), C (4 , -2), D (-4 , -4)
Use the midpoint formula to find midpoints of:
AB
BC
CD
DA
(Is it a special parallelogram? Use slope to check for ║, and distance formula to check side lengths.)
Practice:
HW: p.404 #18-26 even, 31-33, 37-38, 45-50
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 22: Applying Coordinate Geometry (PH text 6.8)
Objective:
to name coordinates of special figures by using their properties
We can use Coordinate Geometry to supply missing information.
1)
Square ABCD
Find the coordinates of the other vertices.
A (-3, 3), B (-3, -3), C (
,
), D (
, )
Hints:
If this is a square, …
What do you know about side lengths?
What do you know about the sides’ relationship to one another?
What do you know about the slope of the sides?
2)
Rhombus EFGH
Find the coordinates of the other vertex.
E (0, 0), F (3, 4), G (8 , 4 ), H (
,
)
Hints:
If this is a rhombus, …
What do you know about side lengths?
What do you know about the diagonals’ relationship to one
another?
What do you know about the slope of the diagonals?
25
Geometry 2206
Unit 3:
3)
Mrs. Bondi
Find the coordinates of the missing vertices of isosceles trapezoid EFGH. EF  GH
E (-1, -2), F (-1, 5), G (4 , 8), H (
,
)
In Coordinate Geometry, we can use variables to name coordinates of a figure. This is
useful to demonstrate a general case for a given situation.
Use variables to name the coordinates of the vertices of each figure.
Square
Isosceles Triangle
Rectangle
Rhombus
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Geometry 2206
Unit 3:
Mrs. Bondi
What do you know about the diagonals of a parallelogram?
How can we find the coordinates of D?
We can use coordinates with variables to prove a general geometric relationships. This is called a
coordinate proof. Sometimes using a coordinate proof is the easiest way to prove a statement.
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Geometry 2206
Unit 3:
Mrs. Bondi
Practice:
HW: p.410 #8-30 even, 38-40
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 23: Proofs Using Coordinate Geometry (PH 6.9)
Objective:
to prove theorems using figures in the coordinate plane
Find the coordinates of the midsegment of trapezoids ABCD and EFGH.
Write a coordinate proof – use coordinate geometry to prove that the midpoint of the hypotenuse of
right
LMN is equidistant from the three vertices. (Hint: use midpoint and distance formulas)
Given:
LMN is a right triangle
L (0, 0), M (2a, 0), N (0, 2b)
P is the midpoint of MN
LP = MP = NP
Prove:
Statement
Reason
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Geometry 2206
Unit 3:
Mrs. Bondi
Statement
Given: MN is the midsegment of
trapezoid TRAP.
Prove: MN||TP, MN||RA,
and MN = ½(TP + RA).
R (2b, 2c)
T (0, 0)
A (2d, 2c)
P (2a, 0)
Practice:
HW: p.416 #4-28 even, 34-40
30
Reason
Geometry 2206
Unit 3:
Mrs. Bondi
31
Geometry 2206
Unit 3:
Mrs. Bondi
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Geometry 2206
Unit 3:
Mrs. Bondi
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Geometry 2206
Unit 3:
Mrs. Bondi
Chapter 6 Review
34
Geometry 2206
Unit 3:
Mrs. Bondi
Chapter 6 Review (continued)
35
Geometry 2206
Unit 3:
Mrs. Bondi
After ch.6 test – get ready for ch.7, p.429, and ch.10, p.611
Additional Review:
1. The lengths of two sides of a polygon are in the ratio 2 : 3. Write expressions for the measures of the two sides in terms
of the variable x.
2. ∆HJK ~ ∆RST. Complete each statement.
3. To the nearest inch, a door is 75 in. tall and 35 in. wide. What is the ratio of the width to the height?
4. What is a proportion that has means 9 and 10 and extremes 6 and 15?
5. Find the geometric mean of each pair of numbers. a. 4 and 25
b. 9 and 12
Solve for the value of the variables in each right triangle.
6.
7.
8.
9.
10.
11.
36
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 24: Proportions in Triangles (PH text 7.5)
Objective:
to use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem
Reminder:
Theorem 7-4
Side-Splitter Theorem
If a line is parallel to one side of a triangle
and intersects the other two sides, then it
divides those sides proportionally.
Example 1: Find the value of x.
Example 2: Find the value of x.
Reminder:
Corollary to Side-Splitter Theorem If three parallel lines
intersect two transversals, then the
segments intercepted on the transversals
are proportional.
Example 3: Find the value of x and y.
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Geometry 2206
Unit 3:
Mrs. Bondi
Theorem 7-5
Triangle-Angle-Bisector Theorem
If a ray bisects an angle of a triangle,
then it divides the opposite side into
two segments that are proportional to
the other two sides of the triangle.
Examples:
4. Find the value of x.
9
5. Find the value of x.
5
6
15
X
3
6. Find the value of x.
7. Find the value of x.
3 cm
15 cm
7 cm
8
x
30
Practice:
HW: p.474 #8-40 even, 46-47
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 25: Areas of Parallelograms and Triangles (PH text 10.1)
Objective:
to find areas of parallelograms and triangles
Theorem 10-1
Area of a Rectangle
A = _________
Theorem 10-2
Area of a Parallelogram
A = _________
Theorem 10-3
Area of a Triangle
A = _________
Base of a parallelogram
Altitude
Height
Examples:
1. Find the area and perimeter of:
15 cm
2. Find the area of the shaded triangular region.
12 cm
3 ft
20 cm
2 ft
2 ft
3. Abby’s Bakery has a plan for a 50’ by 31’ rectangular parking lot. The four parking spaces are
congruent parallelograms (10 ft by 16 ft), the driving area is a rectangle, and the two unpaved areas for
flowers are congruent triangles.
a) Complete the diagram based on the description.
50'
31'
b) Explain two different ways to find the area of the region that must be paved.
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Geometry 2206
Unit 3:
Mrs. Bondi
4. In a triangle, a base and the corresponding height are in the ratio 3:2. If the area is 108 in2,
determine the length of the base and its corresponding height.
D
5. Determine the value of x in parallelogram ABCD.
C
X
20"
18"
A
Practice:
HW: p.619 #8-34 even, 39-43
40
30"
B
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 26: Areas of Trapezoids, Rhombuses and Kites (PH text 10.2)
Objective:
to find the area of a trapezoid, rhombus or kite
Trapezoid -
base
b1
base –
leg
leg
h
leg –
b2
base
height –
Theorem 10-4
Area of a Trapezoid
The area of trapezoid is half the product of the height and the sum of the lengths
of the bases.
b1
b2
1
A  hb1  b2 
2
h
b2
b1
Examples:
1.
Find the area of a trapezoid with a height of 42 in. and bases measuring 121 in. and 145 in.
2.
B
C
Find the area of Trapezoid ABCD.
BC = 21 cm
AD = 25 cm
60
A
D
Isosceles Trapezoid -
>
P
T
41
Z
>
A
E
R
Geometry 2206
Unit 3:
Mrs. Bondi
>
P
Examples:
3. Find the area of trapezoid TRAP
if ET = 15 ft and AP = 10 ft.
>
T
H
A
45
10 2 ft
45
E
6 cm
R
T
4. Find the area of isosceles trapezoid NRTH.
Leave your answer in simplest radical form.
60
N
2 cm
O
5. The area of a trapezoid is 160 cm 2 . Its height is
8 cm and the length of its shorter base is 14 cm.
Find the length of the longer base.
Theorem 10-5
Area of a Kite
The area of rhombus or a kite is half the product of the lengths of its diagonals.
A
Problem:
a)
b)
1
d1d 2
2
Find the measures of the numbered angles in the rhombus. (justify each)
1
A  d1 d 2
Find the area. BE = 5cm; CE = 6 cm
B
C
2
1
Justify each step.
E
4
3
2
A
D
42
R
Geometry 2206
Unit 3:
Mrs. Bondi
K
Examples:
6. Find the area of kite KITE if EI = 10 ft.,
KM = 3 ft., and KT = 14 ft.
E
M
T
7.
Find the area of the given figure.
Practice:
HW: p.626 #12-38 even, 43-45
43
I
Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 27: Areas of Regular Polygons (PH text 10.3)
Objective:
to find the area of a regular polygon
Regular Polygon –
Center –
Radius –
Apothem –
Postulate 10-1
If two figures are congruent, then their areas are equal.
Theorem 10-6
Area of a Regular Polygon
The area of a regular polygon is half the product of the apothem and the
perimeter.
A=
1
ap
a=
A  ap or A 
2
2
p=
Examples:
1)
Find the area of a regular heptagon with a 12 inch apothem, and 10 inch sides.
2)
Find the area of a regular decagon with a 9.4 inch apothem, and 9 inch sides.
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Geometry 2206
Unit 3:
Mrs. Bondi
1)
The length of an apothem of an equilateral triangle is 7 cm. Find the area.
2)
The length of a radius of a regular hexagon is 8 cm. Find the area.
Practice:
HW: p.632 #8-34 even, 44-47
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 28: Perimeters and Areas of Similar Figures (PH text 10.4)
Objective:
to find the relationships between the similarity ratio and the perimeters and
areas of similar figures.
Theorem 10-6
If the scale factor of two similar figures is a:b, then:
a)
the ratio of their perimeters is a:b
b)
the ratio of their areas is a2:b2
Example 1
Find the area of a regular hexagon with side length 3 cm, then find the area of a
regular hexagon with side lengths of 6 cm.
3cm
3cm
6cm
Example 2
The areas of two similar rectangles are 48 in2 and 75 in2. What is the ratio of
their perimeter (scale factor)?
Example 3
Madeline used 144 tiles to tile a rectangular kitchen floor. If each dimension of
the kitchen were doubled, what is the ratio of the perimeters?
X
What is the ratio of the areas?
Y
How many tiles would Madeline need to cover the bigger floor?
2X
2Y
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Geometry 2206
Unit 3:
Mrs. Bondi
Example 4
The areas of two similar rectangles are 1875 ft2 and 135 ft2.
Find the ratio of their perimeters.
Example 5
The similarity ratio of the dimensions of two similar pieces of window
glass is 3:5. If the smaller piece cost $2.50, what should be the cost of the larger
piece (based on area)?
Practice:
47
Geometry 2206
Unit 3:
Mrs. Bondi
Practice:
HW: p.638 #10-46 even, 48-51
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 29a: Trigonometry and Area (PH text 10.5)
Objective:
to find areas of regular polygons and triangles using trigonometry
The apothem of any regular polygon forms isosceles triangles. You can use trigonometry to help find
the area of any regular polygon as long as you know the length of a side, radius or apothem.
Reminder:
Area of a Regular Polygon
A
1
ap
2
or
A
ap
2
Finding area using trigonometry:
Steps:
1. Draw in one apothem and the associated isosceles triangle.
2. Imagine all of these triangles formed within the figure.
3. Divide to find the measure of the angle formed in the right angle
at the center, x.
4. Use trigonometry, the given information and the angle measure
to find the needed information to compute the area.
5. Compute the area of the polygon. It is best to write out what you
will plug into the calculator so you can double check your
accuracy.
Examples:
1.
2.
3
HW. p.646 #6-12 even, 20, 24, 26
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Geometry 2206
Unit 3:
Mrs. Bondi
Lesson 29b: Trigonometry and Area (PH text 10.5)
Objective:
to find areas of regular polygons and triangles using trigonometry
Examples/Practice:
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Geometry 2206
Unit 3:
Mrs. Bondi
Additional Practice:
The polygons are regular polygons. Find the area of the shaded region.
Then find the probability of a pebble, being randomly tossed, hitting the white area.
HW: p.646 #14-18 even, 28, 30, 35-36
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Geometry 2206
Unit 3:
Mrs. Bondi
Review 3.24-29 (text 7.5 & 10.1-5)
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Geometry 2206
Unit 3:
Mrs. Bondi
13. What is the area of the 12-gon with a radius of 8 cm?
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Geometry 2206
Unit 3:
Mrs. Bondi
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