# Parts of a Right Triangle and the Pythagorean Theorem .pdf

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Parts of a Right Triangle and the Pythagorean Theorem

Right Triangle - Triangle with one right angle.

right-angled triangle (British English) is a triangle in which one angle is

a right angle (that is, a 90-degree angle). The relation between the sides and

angles of a right triangle is the basis for trigonometry.

The angles of a right triangle are named using uppercase letters, with C usually used for the right

angle and A and B for the other acute angles.

Angles are also labeled with greek like α, θ, and β, while sides are labeled with lower case letters

like a, b and c.

The longest side that is opposite the right angle is the hypotenuse and the sides, are also called

legs , are referred to as adjacent and opposite sides .

The Right Triangle ABC in the figure has the following parts :

Angles A, B, and C with C as the right angle.

Angles A and B can also be named ∠ α and ∠ β,

respectively .

Side BA or side C is the HYPOTENUSE.

Side CA is the side adjacent to angle α.

Side BC is the side opposite angle α.

The Pythagorean Theorem – relates the three sides of a right triangle.

- This theorem states that” the sum of the squares of two legs of a

right triangle is equal to the square of the hypotenuse” or

c2= a2 + b2

Where c is the hypotenuse and a and b are the legs.

Given the measures of two sides of a right triangle , you can find the measure of the third side by

applying the Pythagorean Theorem

EXAMPLE:

SOLVING FOR THE SIDE OF A RIGHT TRIANGLE USUNG THE

PYTHAGOREAN THEOREM

B

The dimension of a letter – sized bond paper is 8.5 inches

by 11 inches 9 see figure )solve for the length of the

diagonal using the Pythagorean Theorem .

11

α

C

GIVEN:

a= 11

b

C

8.5

b = 8.5

C= ?

SOLUTION : Figure shows that the diagonal c forms two right

triangles.

A

With c as the hypotenuse. To find the length of c, use the

PYTHAGOREAN THEOREM c2= a2 + b2

SOLVING:

c2= a2 + b2

√

√

√

c=13.9

Thus, the length of the diagonal is approximately 13.9

inches .

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