Pythagorean Theorem
32.9
A 35 foot ladder is leaned against a wall. If the base of the ladder is 12 feet from the wall, how many feet high will the ladder reach?
about 113.1
A baseball diamond is a square with sides of 80 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?
Diagonal of a square
A line segment connecting opposite vertices of the square.
Theorem
A mathematical statement that can be proven using definitions, postulates, and other theorems.
25
A rectangle measures 24 in by 7 in. What is the length of its diagonal?
24 cm
A right triangle has a leg that measures 10 m. Its hypotenuse is 26 m. What is the length of the missing leg?
17
A right triangle has legs that measure 8 cm and 15 cm. What is the length of the third side?
Proof
A series of steps used to prove the validity of an if-then statement
36
Find the perimeter of the triangle.
about 10.6
Find the value of x.
about 14.3
Find the value of x.
about 15.8
Find the value of x.
about 18.9
Find the value of x.
About 11.18
The lengths of the legs of a right triangle are 10 and 5. What is the length of the hypotenuse?
27.2
A suitcase measures 22 inches long and 16 inches high. What is the diagonal length of the suitcase to the nearest tenth of a foot?
Right triangle
A triangle with one right angle
about 16.6
An 18 ft string is tied to the top of a pole and pulled to the ground 7ft away from the pole. How tall is the pole?
Right angle
An angle that has a measure of 90 degrees (indicated by a square drawn at the corner formed by the angle)
Leg
Either of the two shorter sides of a right triangle
about 8.3
Find the value of x.
8
Given that the hypotenuse of a right triangle is 10 cm and one leg measures 6 cm, what is the length of the other leg?
Pythagorean Theorem
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a² + b² = c².
6
Peter regularly takes a short-cut across Mr. Henry's lawn instead of walking on the sidewalk (8 m by 15 m) on his way home from school. How many meters is saved by Joe cutting across the lawn?
20
The diagonal of a rectangle is 25 cm. The width is 15 cm. What is the length?
about 11.5
The length of a rectangle is 8 cm. Its diagonal measures 14 cm. What is its width?
2.5
The lengths of the legs of a right triangle are 1.5 and 2. What is the length of the hypotenuse?
50
The lengths of the legs of a right triangle are 14 and 48. What is the length of the hypotenuse?
30
The lengths of the legs of a right triangle are 24 and 18. What is the length of the hypotenuse?
About 18.97
The lengths of the legs of a right triangle are 6 and 18. What is the length of the hypotenuse?
15
The lengths of the legs of a right triangle are 9 and 12. What is the length of the hypotenuse?
Hypotenuse
The longest side of a right triangle that is always opposite the right angle
26
To avoid the pond, Fred must walk 10 meters south and 24 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
Postulate
A mathematical statement that cannot be proven but is considered to be true
about 15.2
Two snails being at the same place in the garden. One snail travels six cm north. Another travels fourteen cm west. How far apart will they be?
13
What is the length of the hypotenuse of a right triangle with legs that measure 5 cm and 12 cm?
26
Which of these side lengths of a right triangle is the hypotenuse? 10, 26, 24
39
Which of these side lengths of a right triangle is the hypotenuse? 15, 36, 39
20
Which of these side lengths of a right triangle is the hypotenuse? 20, 12, 16
25
Which of these side lengths of a right triangle is the hypotenuse? 25, 15, 20
10
Which of these side lengths of a right triangle is the hypotenuse? 6, 8, 10
17
Which of these side lengths of a right triangle is the hypotenuse? 9, 12, 17