5-minute check 6
DESCRIPTION
A B C D. 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°. 5-Minute Check 6. Splash Screen. - PowerPoint PPT PresentationTRANSCRIPT
Over Lesson 10–3
A. A
B. B
C. C
D. D
A. 50°, 80°, 50°
B. 40°, 100°, 40°
C. 30°, 120°, 30°
D. 20°, 140°, 20°
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?
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.
• legs
• hypotenuse
• Pythagorean Theorem
• solving a right triangle
• converse
The sides that form a right angle in a right triangle
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
Find the Hypotenuse Length
Find the length of the hypotenuse of the right triangle.
c2 = a2 + b2Pythagorean Theorem
c2 = 212 + 202 Replace a with 21 and b with 20.
c2 = 441 + 400 Evaluate 212 and 202.
c2 = 841 Add 441 and 400.
Answer: The length of the hypotenuse is 29 feet.
Definition of square root
Use the principal square root.
A. A
B. B
C. C
D. D
A. 25 m
B. 12.5 m
C. 5 m
D. 2.6 m
Find the length of the hypotenuse of the right triangle.
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 ItemMake a drawing to illustrate the problem. The ladder, ground, and side of the house form a right triangle.
Solve the Test ItemUse the Pythagorean Theorem to find the length of the ladder.
c2 = a2 + b2Pythagorean Theorem
Answer: The ladder is about 10.4 feet tall.
c2 = 32 + 102 Replace a with 3 and b with 10.
c2 = 9 + 100 Evaluate 32 and 102.
c2 = 109 Simplify.
Use the principal square root.
Definition of square root
A. A
B. B
C. C
D. D
A. 11.6 feet
B. 10.9 feet
C. 11.3 feet
D. 11.1 feet
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?
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?
322 = 242 + b2 Replace c with 32 and a with 24.
c2 = a2 + b2Pythagorean Theorem
1024 = 576 + b2 Evaluate 322 and 242.
448 = b2 Subtract 576 from each side.
The diagonal is the hypotenuse of a right triangle. The length and width are the sides.
Solve a Right Triangle
Definition of square root.
Use a calculator.
Answer: The garden is about 21.2 feet wide.
ENTER2nd 448 21.16601049
A. A
B. B
C. C
D. D
A. 26.5 feet
B. 35 feet
C. 50 feet
D. 61.2 feet
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?
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
Answer: The triangle is not a right triangle.
c2 = a2 + b2Pythagorean Theorem
6084 = 2304 + 3600 Evaluate 782, 482, and 602.
?
? 782 = 482 + 602 Replace c
with 78, a with 48, and b with 60.
6084 ≠ 5904 Simplify.
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
Answer: The triangle is a right triangle.
c2 = a2 + b2Pythagorean Theorem
5476 = 576 + 4900 Evaluate 742, 242, and 702.
?
? 742 = 242 + 702 Replace c
with 74, a with 24, and b with 70.
5476 = 5476 Simplify.
A. A
B. B
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. A
B. B
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.
