Upload
harvey-clement-oconnor
View
241
Download
1
Tags:
Embed Size (px)
Citation preview
Geometric Shapes
Lesson 1
Triangles Triangles Triangles
Let’s Discover:Triangle Cut-Apart
What do you know about triangles?
Characteristics of triangle “angles”:
The sum of the angles in any size triangle is equal
to 1800.
90
55
35
90 + 35 + 55 = 180
Example 1:
80
45
x
Example 2:
Now try these:
In triangle ABC, m ∠ CAB = 57
and m ∠ ABC = 104. Find m ∠ ACB.
EXIT CARD:
If you have angles 30 and 80 degrees, what is the
measure of the third angle?
Lesson 2
Angles Angles Angles
Brainpop Video
“Types of Triangles”
Characteristics of triangle “sides”:
The sum of the two smaller sides must be
greater than the length of the third side.
Example 1:
Can the following lengths make a triangle?
4 cm, 8 cm, 14 cm
4 + 8 = 12 12 ‹ 14 so no these sides cannot make a triangle.
Can the following lengths make a triangle?
5 in, 10 in, 13 in
Example 2:
5 + 10 = 15 15 › 13 so these sides do make a triangle.
Does the following lengths form a triangle?
a. 7 ft, 19 ft, 15 ft
b. 24 mm, 20 mm, 30 mm
c. 15 in, 25 in, 45 in
d. 4 cm, 12 cm, 18 cm
e. 1 yd, 10 yd, 20 yd
Exit Card:
3-2-1
Adjacent, Vertical,
Supplementary, and Complementary Angles
Adjacent angles are “side by side” and share a common ray.
45º15º
These are examples of adjacent angles.
55º
35º
50º130º
80º 45º
85º20º
These angles are NOT adjacent.
45º55º
50º100º
35º
35º
When 2 lines intersect, they make vertical angles.
75º
75º
105º105º
Vertical angles are opposite one another.
75º
75º
105º105º
Vertical angles are opposite one another.
75º
75º
105º105º
Vertical angles are congruent (equal).
30º150º
150º30º
Supplementary angles add up to 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
Practice Time!
Directions: Identify each pair of angles as
vertical, supplementary, complementary,
or none of the above.
#1
60º120º
#1
60º120º
Supplementary Angles
#2
60º30º
#2
60º30º
Complementary Angles
#3
75º75º
#3
75º75º
Vertical Angles
#4
60º40º
#4
60º40º
None of the above
#5
60º
60º
#5
60º
60º
Vertical Angles
#6
45º135º
#6
45º135º
Supplementary Angles
#7
65º
25º
#7
65º
25º
Complementary Angles
#8
50º90º
#8
50º90º
None of the above
Directions:Determine the missing angle.
#1
45º?º
#1
45º135º
#2
65º
?º
#2
65º
25º
#3
35º
?º
#3
35º
35º
#4
50º
?º
#4
50º
130º
#5
140º
?º
#5
140º
140º
#6
40º
?º
#6
40º
50º
Circle Review:A circle is the set of points that are all an equal distance from a point called the center.
The diameter is twice the radius. d = 2r
The radius is half of the diameter. r = d/2.
Pi (π) is approximately 3.14
Circumference of a circle can be found using
C = πd or C = 2πr
Area of a circle can be found using the formula A = πr2
Mr. Smith has a garden that is in the shape of a circle. There is a path 5 feet in length that goes from the center of the garden to the edge of the garden. If
Mr. Smith wants to add a path across the garden, how long will it be?
Radius (r)
Diameter (d)
The diameter is twice the radius.d = 2r
The radius is half of the diameter. r = d/2
Since d = 2r
d = 2(5ft)
d = 10ft
Find the radius of a circle that has a diameter of 7 inches.
r = d/2
r = 7/2
r =3.5 inches
A circle has a radius of 12 meters. What is the diameter of the circle?
Find the radius of a circle with a diameter of 15 centimeters.
A circle has a diameter of 12 feet. What is the length of the radius?
How do you find the circumference of a circle?
Pi, represented by the symbol π, is a constant ratio that relates circumference and diameter.
Pi is approximated as 3.14
To find the circumference, we use one of the formulas:
C =πd or C = 2πr
What is the circumference of a circle that has a radius of 8 centimeters? Do not approximate pi.
C = 2πr
C = (2)π(8 cm)
C = 16π cm
A circle has a radius of 6 inches. What is the circumference of the circle? Do not approximate pi.
A circle has a diameter of 8 meters. What is the circumference of the circle? Use 3.14 for pi.
A circle has a radius of 7 feet. Find the circumference of the circle. Do not approximate pi.
How do you find the area of a circle?
Area of a circle can be found by using the formula
A = πr2
A pizza has a radius of 9 inches. What is the area of the pizza?
r = 9 inches
A = π(9in.)2
A = 3.14(81in.2)
A = 254.34in.2
Find the area of a circle with a diameter of 10 meters. Do not approximate pi.
A = π(5m)2
A = 25πm2
What is the area of a circle that has a radius of 6 cm? Use 3.14 for pi.
Susan drew a circle with a radius of 4 inches and Ellen drew a circle with a radius of 8 inches. Ellen said “since the radius of my circle with twice the radius of your circle, the area of my circle is twice the area of your circle.” Is Ellen’s statement correct? If not, explain what Ellen could say instead.
A circle is inside of a square, as shown below. The edges of the square each touch a point on the circle. If the square has an area of 16 square meters, what is the area of the circle?
A circular pizza can feed 4 people if it has an area of at least 200 square inches. A pizza
from Joe’s Pizza has a radius of 9 inches. Is it enough to feed a family of 4?
How do you find the area of the circle if you only know the circumference?
Area of a Circle = πr2
Circumference of a Circle= πd or 2πr
A playground in the shape of a circle has a circumference of 18π yards. What is the area of the
playground?C = 18π yds.
C = πd
D = 18 yds 18 yds
Area = π(9 yds)2
Diameter = 18 yards
Radius = 9 yards
Area = 81π yds2
18 yds
9 yds
A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle?
C = πd
37.68cm = 3.14d
37.68cm = 3.14d
3.14 3.14
d = 12 cm
d = 12 cm r = 6 cm
A = 3.14(6cm)2
A = 3.14(36cm2)
A = 113.04 cm2
A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle?
The circumference of a circle is 10π. What is the area of the circle?
The circumference of a circle is 12.56 ft². If 3.14 was used to approximate pi, what is the area of the circle?
A circle has a circumference of 9π meters. Find the area of the circle.
How can you find the circumference of a circle if you only know the area?
Area of a Circle = πr2
Circumference of a Circle= πd or 2πr
The reverse of squaring a number is finding the square root.
32 = 9
Bill has a circular garden that he wants to put a fence around. He knows that the area of a garden is 16π
yds2. How much fencing does Bill need to go around the circumference of the garden?
A = 16π yds2
A = πr2 C = 2πr
r2 = 16 yds2
r = 4 yds 4 yds
C = 2π(4 yds)
C = 8π yds
A circle has an area of 25π cm2. What is the circumference of the circle?
The area of a circle is 16π meters2. Stephanie concluded that the circumference of the circle would be 16π. She stated “the radius would be 8 meters since the square root of 16 is 8.” What mistake did Stephanie make. Write an explanation describing how to fix her mistake.
A circle inside of a square touches the square at each edge as shown below. If the circle has an area of 25π feet2, find the area of the square.
Find the circumference of the circle that has an area of 81π m2.
A circle has an area of 113.04 cm2. What is the circumference of the circle?