7.1 Apply the Pythagorean Theorem

Parts of a Right triangle Hypotenuse – opposite the right angle and the longest side Legs – the sides that form the right angle

Pythagorean Theorem The theorem says that of I square the legs of a right triangle and add them they will be equal to the hypotenuse squared

Pythagorean Theorem

A couple of examples solved

Pythagorean triples A Pythagorean triple are integers(whole numbers) that exactly fit the Pythagorean theorem. The simplest of which is 3,4,5 where 3 and 4 are legs and 5 is the hypotenuse

A list of some of the Pythagorean triples

Finding the area of an isosceles triangle In the figure below, finding are is easy! A = 1/2bh A = ½ 12*6 A = 36

Area of an isosceles triangle In this figure it requires a little more thought! How do I find Height?

Area of an isosceles triangle If you recall, the altitude of a triangle is perpendicular to the base

Area of an isosceles triangle In an isosceles triangle, an altitude from the vertex angle will bisect the opposite side Do you see two right triangles!

Area of an isosceles triangle

I now have height so……. A = ½ 12*10 or 60

Area of a composite figure Notice the figure is made of a rectangle and two right triangles I need to find the are of the square and at least one of the triangles Use the Pythagorean theorem to find the other side of the rectangle

Composite figure