Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

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Presentation transcript:

Special Right Triangles

Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

Right Isosceles Triangle s s Leg Leg Hyp

Leg 1-If the perimeter of the square is 28, what is the length of the diagonal? 2- If the diagonal has a length of 12, what is the perimeter of the square? Area? The diagonal of a square is the Hypotenuse of two isosceles right triangles. 1- Perimeter = 28 4x = 28 x = 7 Leg = 7 Hyp = 7  2 2- Diagonal = 12 Leg = 12÷  2 = 6  2 P = 4(6  2) =24  2 A = 6  2·6  2 = 72

Long Leg Short Leg Hypotenuse Know the Short Leg (SL): Hypotenuse = 2 · SL Long Leg = Know Hypotenuse: Short leg = ½ Hypotenuse Know Long Leg (LL): Short leg = 30° 60°

x 2x Short Leg Long Leg Hyp

When you draw the altitude of an equilateral triangle, you create two triangles. The triangle side length is the hypotenuse of the Half of the side length is the short leg of the The altitude, then, is half the triangle side times the square root of 3. 60° 30° x 2x 30°