quiz 1. find the perimeter of the figure. 2. find the area of the figure. 12 ft 4 ft5 ft 3. the...
TRANSCRIPT
Quiz1. Find the perimeter of the figure.
2. Find the area of the figure.
12 ft
12 ft
4 ft5 ft
5 ft
5 ft
5 ft
3. The perimeter of the triangle
4. The perimeter of the combined figure
5. The area of the trapezoid
Pre-Algebra
6.3
The Pythagorean Theorem
Graph the figures with the given verticals and find the area.
1. (–1, –1), (–1, 3), (6, –1)
2. (2, 1), (8, 1), (6, –3)
3. (3, –2), (15, –2), (14, 6), (4, 6)
14 units2
12 units2
88 units2
Warm Up
Learn to use the Pythagorean Theorem and its converse to solve problems.
Pythagorean Theorem
leg
hypotenuse
Vocabulary
a2 + b2 = c2
4
5
c
6.40 c
A.
Pythagorean TheoremSubstitute for a and b.
a2 + b2 = c2
42 + 52 = c2
16 + 25 = c2
41 = c
Simplify powers. Solve for c; c = c2.
Find the length of the hypotenuse.
41 = c2
Example: Find the the Length of a Hypotenuse
15 = c
B.
Pythagorean TheoremSubstitute for a and b.
a2 + b2 = c2
92 + 122 = c2
81 + 141 = c2
225 = cSimplify powers. Solve for c; c = c2.
Find the length of the hypotenuse.
triangle with coordinates
(1, –2), (1, 7), and (13, –2)
Example: Find the the Length of a Hypotenuse
5
7
cA.
Find the length of the hypotenuse.
8.60 c
Pythagorean TheoremSubstitute for a and b.
a2 + b2 = c2
52 + 72 = c2
25 + 49 = c2
74 = cSimplify powers. Solve for c; c = c2.
Try This
B. triangle with coordinates (–2, –2), (–2, 4), and (3, –2)
x
y
The points form a right triangle.
(–2, –2)
(–2, 4)
(3, –2)
Find the length of the hypotenuse.
7.81 c
Pythagorean Theorema2 + b2 = c2
62 + 52 = c2
36 + 25 = c2
61 = cSimplify powers. Solve for c; c = c2.
Substitute for a and b.
Try This
25
7
b
576 = 24b = 24
a2 + b2 = c2
72 + b2 = 252
49 + b2 = 625–49 –49
b2 = 576
Solve for the unknown side in the right triangle.
Pythagorean TheoremSubstitute for a and c. Simplify powers.
Example: Finding the Length of a Leg in a Right Triangle
b 11.31
12
4
ba2 + b2 = c2
42 + b2 = 122
16 + b2 = 144–16 –16
b2 = 128
128 11.31
Solve for the unknown side in the right triangle.
Pythagorean TheoremSubstitute for a and c. Simplify powers.
Try This
a6 6
4 4
a2 + b2 = c2
a2 + 42 = 62
a2 + 16 = 36
a2 = 20a = 20 units ≈ 4.47 units
Find the square root of both sides.
Substitute for b and c.Pythagorean Theorem
A = hb = (8)( 20) = 4 20 units2 17.89 units212
12
Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle.
Example: Using the Pythagorean Theorem to Find Area
a2 + b2 = c2
a2 + 22 = 52
a2 + 4 = 25
a2 = 21
a = 21 units ≈ 4.58 units
Find the square root of both sides.
Substitute for b and c.
Pythagorean Theorem
A = hb = (4)( 21) = 2 21 units2 4.58 units212
12
Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle.
a5 5
2 2
Try This
1. Find the height of the triangle.
2. Find the length of side c to the nearest meter.
3. Find the area of the largest triangle.
4. One leg of a right triangle is 48 units long, and the hypotenuse is 50 units long. How long is the other leg?
8m
12m
60m2
14 units
h
c10 m
6 m 9 m
Use the figure for Problems 1-3.Lesson Quiz