triangles triangles triangles let’s discover: triangle cut-apart

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

Lesson 3

http://www.youtube.com/watch?v=GO20ZgUzlc0

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?