Special Right Triangles. Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides.

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Presentation transcript:

Special Right Triangles

Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides are called LEGS Hypotenuse LEG

Pythagorean Theorem The sides of a right triangle satisfy this theorem: a 2 + b 2 = c 2 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: 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: 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 x x x x

Ex. Find the values of the variable(s) s 5 t s 30 60

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