Geometry (Triangles)

Question 1

Right Triangle

Answer 1

A Triangle with a “right” or 90° angle.

Question 2

Hypoteneus

Answer 2

The longest side of a right triangle, opposite the right angle.

Question 3

Pythagorean Theorem

Answer 3

a² + b² = c²

• In a Right Triangle, the area of the square whose side is the “hypotenuse” is equal to the sum of the areas of the squares of the other two sides.

Question 4

Describe Garfields Proof of the Pythagorean Theorem

Answer 4

1. Construct a right triangle with Length “B,” Height “A,” and Hypotenuse “C.”
2. Create a Congruent Triangle (Stacked on Top) creating a side “A + B” as the height.
3. Label the Angles and Prove that the missing Angle = 90°.
4. Create an equation using the Area of a Trapezoid,

Height x ((Top Base + Bottom Base)/ 2)

5. Create an equation using the Area of the Triangles,

(Base x Height) / 2 and simplify both as a single equation.

Question 5

Find the “x” value in the triangle below.

Answer 5

2√3

Question 6

Find the x value in the triangle below.

Answer 6

x = 13

Question 7

Find the x value in the triangle below.

Answer 7

x = 6

Question 8

Find the x value in the triangle below.

Answer 8

x = 8

Question 9

45°-45°-90° Triangle Equation for the Hypotenuse

Answer 9

A = B = (√2/2) C

or

(√2) A = (√2) B = C

Question 10

Find the length of the unknown sides in the triangle shown below

Answer 10

8√2

Question 11

Find the length of the unknown sides in the triangle shown below

Answer 11

5√2

Question 12

Create a Proof for the 45°-45°-90° Triangle Equation

Answer 12

1. Establish that a 45°-45°-90° Triangle has two equal length sides.
2. From that information we can Establish that in the Pythagorean Theorem, A = B, and we can Substitute one with the other.
3. Simplify the equation and solve for A or B to determine that

A = B = (√2/2) C

or

(√2) A = (√2) B = C

Question 13

Destinguishing a 45° 45° 90° Triangle

Answer 13

1. The two sides that aren’t the hyptotenuse will be the same length
2. When given the hypotenuse, the other side of the triangle will be half the length of the Hypotenuse multiplied by √2.
3. To find the hypotenuse just multiply the a leg of the Triangle by √2.

Question 14

Destinguishing the three sides of a 30° 60° 90° Triangle

Answer 14

1. The side opposite the 90° angle is equal to “x.”
2. The side opposite the 30° angle is 1(x)/2.
3. The side opposite the 60° angle is √3(x)/2.

Question 15

Create a proof for the sides of a 30° 60° 90° Triangle.

Answer 15

1. Create an Equilateral Triangle and label all the sides and angles.
2. Split the Equilateral Triangle down the middle and label the new sides and angles.
3. Create an equation using the Pythagorean Theorem to find the missing side.
4. Solve and Simplify the equation for the missing side “a.”

Question 16

Solve for the missing side of the Triangle.

Answer 16

6√3

Question 17

Solve for the missing Sides.

Answer 17

Hypotenuse = 12√3

Side B (opposite 30° angle) = 6√3

Question 18

Solve for the missing Sides.

Answer 18

Side (opposite 60°) = 15√3

Side (opposite 30°) = 15

Question 19

How can you destinguish a 30° 60° 90 °Triangle?

Answer 19

The Hypotenuse will either be (The length of the shortest side multiplied by 2) or (The length of the second longest side divided by √3 then multiplied by two).

The second longest side (opposite the 60° angle) will either be (The length of the shortest side multiplied by √3) or (The length of the hypotenuse divided by two, then multiplied by √3).

The shortest length (opposite the 30° angle) will either be (The length of the hypotenuse divided by 2) or (The length of the second longest side divided by √3).

Question 20

How do you find the area of a Triangle?

Answer 20

Multiply the base of the Triangle by the height, then divide by 2.