Warm Up Find the value of x. Leave your answer in simplest radical form. 7 x 9 x 7 9.

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Objectives Justify and apply properties of 45°-45°-90° triangles.

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Presentation transcript:

Warm Up Find the value of x. Leave your answer in simplest radical form. 7 x 9 x 7 9

7.3: Special Right Triangles Objectives: To use the properties of and right triangles

45°-45°-90° Right Triangle It is an isosceles, right triangle– Both legs are congruent!! THEOREM: The hypotenuse is times the length of the legs IF YOU NEED TO FIND THE HYPOTENUSE: Hypotenuse = (Length of Leg) X IF YOU NEED TO FIND A LEG: Length of leg =

Examples: 1.Find h:2. Find x: 9 h x

Find x: x

x x

Find x: 10 x

A square has a perimeter of 24 inches. How long is the diagonal?

30°-60°-90° Right Triangle  Shorter Leg is the side opposite the 30° angle  Longer leg is the side opposite the 60° angle Let the shorter leg = n HYPOTENUSE = 2 ∙ SHORTER LEG = 2n LONGER LEG = SHORTER LEG = n

If you need to find the shorter leg (side opposite 30°): If given the hypotenuse: SHORTER LEG = If given the longer leg: SHORTER LEG=

Fill in the table of values for the side lengths of a triangle: Shorter LegLonger LegHypotenuse

Find the missing lengths g f 5 x y

Find the variables x y 30 k m

Find the value of each variable. (Figure not drawn to scale) b cd a 4530

Find the value of each variable. Leave your answer in simplest radical form. b a 4 45°

Find the area. Round your answer to the nearest tenth. 60

Find the area of the triangle. 45