Geometry- Pythagorean Theorem

Question 1

What is the Pythagorean Theorem formula?

Answer 1

a^2 + b^2 = c^2.

Question 2

In the formula a^2 + b^2 = c^2, which letter represents the hypotenuse?

Answer 2

c.

Question 3

What is the definition of the Hypotenuse?

Answer 3

The longest side of a right triangle, located opposite the 90-degree angle.

Question 4

Can the Pythagorean Theorem be used on an obtuse triangle?

Answer 4

No. It only works for Right Triangles (90 degree angle).

Question 5

What is a “Pythagorean Triple”?

Answer 5

A set of three positive integers that perfectly fit the a^2 + b^2 = c^2 rule.

Question 6

Identify the most common Pythagorean Triple.

Answer 6

3, 4, 5.

Question 7

If the legs of a right triangle are 6 and 8, what is the hypotenuse?

Answer 7

10 (Triple: 6, 8, 10).

Question 8

Solve for c: a=5, b=12.

Answer 8

c=13 (25 + 144 = 169).

Question 9

Solve for a: c=10, b=6.

Answer 9

a=8.

Question 10

A 13ft ladder leans against a wall. The base is 5ft from the wall. How high does it reach?

Answer 10

12ft.

Question 11

Is 5, 10, 15 a Pythagorean Triple?

Answer 11

No (25 + 100 is not 225).

Question 12

Is 8, 15, 17 a Pythagorean Triple?

Answer 12

Yes (64 + 225 = 289).

Question 13

Is 7, 24, 25 a Pythagorean Triple?

Answer 13

Yes.

Question 14

Is 9, 40, 41 a Pythagorean Triple?

Answer 14

Yes.

Question 15

Find c if a=1, b=1.

Answer 15

Square root of 2.

Question 16

In a square with side length 5, what is the length of the diagonal?

Answer 16

5 * square root of 2.

Question 17

Solve for the missing leg: c=25, a=7.

Answer 17

24.

Question 18

A triangle has sides 9, 12, 15. Is it a right triangle?

Answer 18

Yes (Scale of 3, 4, 5).

Question 19

If you double the sides of a 3-4-5 triangle, what are the new sides?

Answer 19

6, 8, 10.

Question 20

What is the “Converse” of the Pythagorean Theorem?

Answer 20

If a^2 + b^2 = c^2, then the triangle must be a right triangle.

Question 21

Solve for c: a=20, b=21.

Answer 21

c=29.

Question 22

Find the height of an isosceles triangle with sides 10, 10, and base 12.

Answer 22

8 (Creates two 6-8-10 right triangles).

Question 23

A screen is 10 inches wide and 24 inches tall. What is the diagonal length?

Answer 23

26 inches.

Question 24

If c^2 > a^2 + b^2, what type of triangle is it?

Answer 24

Obtuse.

Question 25

If c^2 < a^2 + b^2, what type of triangle is it?

Answer 25

Acute.

Question 26

Find b if a=9, c=15.

Answer 26

12.

Question 27

Find c if a=11, b=60.

Answer 27

61.

Question 28

A hiker walks 3 miles North and 4 miles East. How far is he from the start?

Answer 28

5 miles.

Question 29

Find the distance between (0,0) and (3,4) on a graph.

Answer 29

5.

Question 30

Solve for c: a=12, b=16.

Answer 30

20.

Question 31

Solve for c: a=8, b=15.

Answer 31

17.

Question 32

If a rectangle has a diagonal of 5 and a width of 3, what is the length?

Answer 32

4.

Question 33

If a=b, the triangle is a --__ triangle.

Answer 33

45-45-90.

Question 34

In a 45-45-90 triangle, c is always __ times the leg.

Answer 34

square root of 2.

Question 35

Solve for c if a=10, b=24.

Answer 35

26.

Question 36

Solve for b if a=48, c=50.

Answer 36

14.

Question 37

Solve for c if a=1.5, b=2.

Answer 37

2.5.

Question 38

Can a, b, or c be negative?

Answer 38

No, they represent physical lengths.

Question 39

Solve for c: a=12, b=35.

Answer 39

37.

Question 40

What side is always the longest?

Answer 40

The hypotenuse (c).