Vocabulary
Distance
Pythagorean Theorem
Converse of Pythagorean Theorem
Story Problems
100
The Pythagorean Theorem can only be used on what type of triangles?
Right
100
What can we use to find the distance of two points?
Pythagorean Theorem (or right triangle)
100
What is the value of x?
10
100
Would a triangle with side lengths 6, 8, and 10 inches form a right triangle?
Yes
100
Sally walks away from her house. She walks 8 m west then 15 m south. How far, in meters, is she from her house?
17 meters
200
In the Pythagorean Theorem, "b" stands for the ________.
Base/Leg
200
Find the distance between these two points: (3, 7) and (15, 7)
12 units
200
Both legs are 6 and 20. Find the hypotenuse (round to the nearest tenth).
c=sqrt436approx20.9 units
200
In order to ensure that the roof consists of right angles, an architect measures the diagonal to create a triangle. If the dimensions of the triangle are 9.5 feet, 16 feet, and 18.5 feet, is the triangle a right triangle?
No
200
An envelope is 11 inches wide and measures 19 inches along the diagonal. How tall, in inches, is the envelope? Round to nearest tenth.
About 15.5 inches
300
In the Pythagorean Theorem, the longest side of a right triangle is called the ________. This is represented by the letter "c".
Hypotenuse.
300
Find the distance between (-10, -6) and (-10, -2)
4 units
300
What is the length of the ground to the base of the ladder?
5 m
300
Would a triangle with side lengths 5 in., 12 in., and 13 in. form a right triangle? Justify your answer.
Yes
5^2+12^2=25+144=169=13^2
300
A 13 foot ladder is placed 5 feet away from a wall. How many feet up the wall will the ladder reach?
12 feet
400
In the Pythagorean Theorem, which leg is "a"?
It doesn't matter which leg, as long as it is a leg!
400
Find the distance between these two points: (4, -5) (-1, 7)
13 units
400
Find the missing leg, if two sides are 12 and 15.
a = 9.
400
Three cities form a triangle. Tom measures the distance between the three cities on a map. The distance between the three cities are 45 miles, 56 miles, and 72 miles. Is the triangle formed by the three cities a right triangle? Justify your answer.
No. The sum of the leg squared = 5,161 and the hypotenuse squared = 5,184.
400
Ed is flying a kite with a string 25 meters long. If his friend is directly under the kite 10 meters away, how high, in meters, is the kite off the ground? Round to nearest tenth.
About 22.9 m
500
Can the Pythagorean Theorem be used to isosceles right triangle?
Yes, because it is a right triangle.
500
Find the distance between two points. Round to the nearest tenth: (2, -9) (-1, 4)
About 13.3 units
500
Find the missing LEG for a right triangle with a = 6 and c = 9.
sqrt45approx6.71units
500
The distance between each base on a softball field is 60 feet. Maddie is placing the bases and measures the distance between home plate and second base. She determines the distance to be 80 feet. Are the bases at right angles? Explain.
No.
60^2+60^2=7200ne80^2=6400
500
Jonny has a boat that averages 5 miles per gallon of gasoline and the tank holds 18 gallons of gasoline. At 10 a.m., he left the dock. At 11 a.m. he was 8 miles east and 15 miles south of the dock. If he continues at this rate, how many more hours will the tank be out of gasoline? Round to the nearest tenth if necessary.
About 4.3 hours more