Download 7.1 Apply the Pythagorean Theorem

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
• 𝑎2 +𝑏 2 =𝑐 2
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 can now use the Pythagorean theorem to
solve for the height
• 62 + ℎ2 = 82 can be written as 82 − 62 =ℎ2
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
• Find the missing side of the rectangle using
Pythagorean theorem
• 26+18+18 = 62
• 302 − 182 = 576
• 24 is the square root of 576
• Find the area of the rectangle
• Find the area of the two triangles
• 24*26+2(1/2*18*24) = 432𝑚2 is the area