1. Triangle ABC is an isosceles triangle
Triangle ABC is an isosceles triangle. The angle measures of triangle ABC are in the ratio 2:5:2. What are the measures of the angles?
A. 50°, 80°, 50°
B. 40°, 100°, 40°
C. 30°, 120°, 30°
D. 20°, 140°, 20° A B C D
5-Minute Check 6

2. Splash Screen

3. You have already found missing measures of similar triangles
You have already found missing measures of similar triangles. (Lesson 6–7)
Use the Pythagorean Theorem to find the length of a side of a right triangle.
Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.
Then/Now

4. solving a right triangle converse
legs
The sides that form a right angle in a right triangle
hypotenuse
Pythagorean Theorem
solving a right triangle
converse
The side opposite the right angle of a right triangle (the longest side)
If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of
the lengths of the legs or c2 = a2 + b2
Using the Pythagorean Theorem to find the length of the third side of a right triangle, if you know the other two sides
The statement formed by reversing the phrases after if and then in an if-then statement
Vocabulary

5. Concept

6. Find the length of the hypotenuse of the right triangle.
Find the Hypotenuse Length
Find the length of the hypotenuse of the right triangle.
c2 = a2 + b2 Pythagorean Theorem
c2 = Replace a with 21 and b with 20.
c2 = Evaluate 212 and 202.
c2 = 841 Add 441 and 400.
Definition of square root
Use the principal square root.
Answer: The length of the hypotenuse is 29 feet.
Example 1

7. A B C D Find the length of the hypotenuse of the right triangle.
A. 25 m
B m
C. 5 m
D. 2.6 m A B C D
Example 1

8. A ladder positioned against a 10-foot building reaches its top
A ladder positioned against a 10-foot building reaches its top. Its base is 3 feet from the building. About how long is the ladder in feet? Round to the nearest tenth.
Read the Test Item Make a drawing to illustrate the problem. The ladder, ground, and side of the house form a right triangle.
Solve the Test Item Use the Pythagorean Theorem to find the length of the ladder.
Example 2

9. c2 = a2 + b2 Pythagorean Theorem
c2 = Replace a with 3 and b with 10.
c2 = Evaluate 32 and 102.
c2 = 109 Simplify.
Definition of square root
Use the principal square root.
Answer: The ladder is about 10.4 feet tall.
Example 2

10. An 18-foot ladder is placed against a building which is 14 feet tall
An 18-foot ladder is placed against a building which is 14 feet tall. About how far is the base of the ladder from the building?
A feet
B feet
C feet
D feet A B C D
Example 2

11. c2 = a2 + b2 Pythagorean Theorem
Solve a Right Triangle
LANDSCAPING A diagonal path through a rectangular garden is 32 feet long. The length of the garden is 24 feet. About how many feet wide is the garden?
The diagonal is the hypotenuse of a right triangle. The length and width are the sides.
c2 = a2 + b2 Pythagorean Theorem
322 = b2 Replace c with 32 and a with 24.
1024 = b2 Evaluate 322 and 242.
448 = b2 Subtract 576 from each side.
Example 3

12. Definition of square root.
Solve a Right Triangle
Definition of square root.
ENTER
2nd
448
Use a calculator.
Answer: The garden is about 21.2 feet wide.
Example 3

13. LANDSCAPING A diagonal path through a rectangular garden is 40 feet long. The length of the garden is 30 feet long. About how many feet wide is the garden?
A feet
B. 35 feet
C. 50 feet
D feet A B C D
Example 3

14. c2 = a2 + b2 Pythagorean Theorem
Identify a Right Triangle
A. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 48 ft, 60 ft, 78 ft
c2 = a2 + b2 Pythagorean Theorem ?
782 = Replace c with 78, a with 48, and b with 60.
6084 = Evaluate 782, 482, and 602. ?
6084 ≠ 5904 Simplify.
Answer: The triangle is not a right triangle.
Example 4 A

15. c2 = a2 + b2 Pythagorean Theorem
Identify a Right Triangle
B. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 24 cm, 70 cm, 74 cm
c2 = a2 + b2 Pythagorean Theorem ?
742 = Replace c with 74, a with 24, and b with 70.
5476 = Evaluate 742, 242, and 702. ?
5476 = Simplify.
Answer: The triangle is a right triangle.
Example 4

16. A. The measures of three sides of a triangle are given
A. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 42 in., 61 in., 84 in.
A. Yes, the triangle is a right triangle.
B. No, the triangle is not a right triangle. A B
Example 4 CYP A

17. B. The measures of three sides of a triangle are given
B. The measures of three sides of a triangle are given. Determine whether the triangle is a right triangle. 16 m, 30 m, 34 m
A. Yes, the triangle is a right triangle.
B. No, the triangle is not a right triangle. A B
Example 4 CYP B

18. End of the Lesson