1. 19.2 Pythagorean Theorem

2. A right triangle is a triangle that has a right (90 degree) angle
A right triangle is a triangle that has a right (90 degree) angle. The 2 sides that form the right angle are called the legs of the triangle and the side opposite the right angle is called the hypotenuse.
hypotenuse
leg
leg
leg
hypotenuse
leg

3. The Pythagorean Theorem relates the sides of any right triangle
The Pythagorean Theorem relates the sides of any right triangle. If a and b represent the legs and c the hypotenuse, then

4. Find the length of the hypotenuse:c
24 dm
10 dm

5. Find the length of the hypotenuse:
8.00 cm
3.90 cm c

6. Find the length of the missing sideb

7. Find the length of the missing sideb

8. Use the Pythagorean theorem.
How long must a guy wire be to reach from the top of a 15-m telephone pole to a point on the ground 10 m from the foot of the pole?
Use the Pythagorean theorem.
10 m
15 m c

9. There are two special right triangles that we will further explore
There are two special right triangles that we will further explore. They are called a 45, 45, 90 right triangle and a 30, 60 ,90 right triangle. The numbers refer to the measure of the angles in degrees.

10. The 45, 45, 90 triangle is an isosceles triangle which means the two legs have equal measure.
hypotenuse
Since the legs are equal, by the Pyth.Theorem, the hypotenuse has length = leg

11. Find the hypotenuse of an isosceles triangle that has equal sides of 2 m.?
Hypotenuse has length =

12. If the hypotenuse of a 45, 45, 90 triangle is 5 cm long, how long is each leg.?
5 cm
Since hyp = leg

13. An equilateral triangle has 3 equal sides and 3 equal angles that each measures 60 degrees. The height bisects both the angle and opposite side making a 30, 60, 90 triangle. 30
½ side or ½ hypot 60 60

14. Applying the Pythagorean Th
Applying the Pythagorean Th. to this 30, 60, 90 triangles gives the following relations: 30
2x, side opposite right angle or longest side
other leg 60
x, side opposite 30 or short leg

15. Find the missing measures.30
Hyp. = 2(short leg) = 2(7 in) = 14 in
Other leg = short leg ? ? 60
7 in

16. Find the missing measures.60 ?
Other leg = short leg ? 30
8 cm
Hyp. = 2(short leg) = 2( 4.6in) = 9.2 in