Special Right Triangles

• Right triangles have one 90o angle• The longest side is called the HYPOTENUSE

• It is directly across from the 90o

• The other sides are called LEGS

HypotenuseLEG

LEG

Pythagorean Theorem

• The sides of a right triangle satisfy this theorem:

a2 + b2 = c2

LEG Hypotenuse

Pythagorean Theorem Review

Pythagorean Theorem Practice

Converse of the Pythagorean Theorem

Converse of Pythagorean Theorem

Solutions:

Pythagorean Triples

•A Pythagorean triple is a set of nonzero whole numbers a,b and c that satistify the Pythagorean theorem.•3,4,5•5,12,13•8,15,17•7,24,25

Practice

IXL - Pythagorean Inequality Theorems

Special Right Triangle Investigation: 45-45-90

• Draw an isosceles right triangle with legs

that measure 4 cm.

• Use the Pythagorean Theorem to find the length of the hypotenuse. Leave answer in simplest radical form.

• Repeat the steps above for an isosceles right triangle with legs that measure 12 cm.

• Now draw an isosceles right triangle with a hypotenuse that measures 7 cm.

• Use the Pythagorean Theorem to find the length of the congruent legs. Leave your answer in simplest radical form.

Special Right Triangle Investigation: 30-60-90

• Draw an equilateral triangle with side lengths of 6 cm.

• Draw the perpendicular bisector from the top vertex.

• Label the angle measures.

• Use the Pythagorean Theorem to find the height of the triangle. Leave answer in simplest radical form.

• Repeat the steps above for an equilateral triangle with side lengths of 10 cm.

45°- 45°- 90°

• In a 45° - 45° - 90° triangle, both legs are congruent and the length of the hypotenuse is the square root of 2 times the length of the leg.

30° - 60° - 90°

Ex. Find the values of the variable.

1. 2.3

3

x 25 x

7 x

3. 4.

x

24

24

Ex. Find the values of the variable(s).

1. 2.

30

60

6

s

5

ts

30

60

Videos

• 45-45-90 Triangles

• 30-60-90 Triangles

Practice

• Khan Academy

• Kuta Software

• IXL