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
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