1. Aim: What’s so special about a 300-600-900 triangle?
Do Now:
Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC.
What is mA? mB? mACB?
What is mACD? mBCD?
600 C
300 2x 2x A B D 2x

2. Pythagorean Theorem - a2 + b2 = c2
triangle
Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC
What is length of CD in terms of x? C
300 2x 2x
Pythagorean Theorem - a2 + b2 = c2 ? A
600 B x 2x D
x2 + (CD)2 = (2x)2
x2 + (CD)2 = 4x2
(CD)2 = 3x2

3. Pythagorean Theorem - a2 + b2 = c2
triangle
Triangle ABC is equilateral with each side equal to 6 (instead of 2x). CD is an altitude of ABC
What is length of CD? C
300
Pythagorean Theorem - a2 + b2 = c2 6 6 ? A
600 B
32 + (CD)2 = (6)2 3 D
9 + (CD)2 = 36
(CD)2 = 27

4. Review the results of the first two problems.
triangle
Problem 1
Problem 2 A 6 3 C D A C 2x x D 3
300
300
600
600
Review the results of the first two problems.
Can you make any general conclusions?

5. triangle
300 2s
600 s

6. Pythagorean Theorem - a2 + b2 = c2
45o - 45o - 90o triangle
Triangle ABC is an isosceles right triangle with BC =
A. What is mB?
mC?
AB?
AC?
Do Now: C
450 x 2 A B
Pythagorean Theorem - a2 + b2 = c2
x2 + x2 = ( )2
2x = ( )2
2x = 8

7. Pythagorean Theorem - a2 + b2 = c2
45o - 45o - 90o triangle
Triangle ABC is an isosceles right triangle with BC =
A. What AB?
AC?
Do Now: 2 6 6 C 2 6 x A B
Pythagorean Theorem - a2 + b2 = c2
x2 + x2 = ( )2 2 6
2x = 72
x = 36
x = 6

8. Review the results of the first two problems.
triangle
Problem 1
Problem 2 C C 2 6 A B A B
Review the results of the first two problems.
Can you make any general conclusions?

9. triangle
In a triangle, the length of the hypotenuse is times the length of a leg.
450 s
450 s
Ratio of Hypotenuse : Leg of I.R.T is always

10. Isosceles Right TriangleBF AB
= = 2
450 CG AC
= = 2 DH AD
= = 2 EI AE
= = 2
Ratio of Hypotenuse : Leg of I.R.T is always

11. Summary of Special Angles in Trig

12. Triangle ABC is a 30-60-90 triangle with BC = 7 A. What is length of
Model Problem
Triangle ABC is a triangle with BC = 7
A. What is length of
AB?
AC?
Do Now: C
300 7
3.5 A
600 B
3.5
Hypotenuse is 2 times the shorter leg
CB = 2(AB)
7 = 2(AB)
3.5 = AB
Longer leg is times the shorter leg
AC = (AB) 3
AC = (3.5) 3
AC  6.06

13. Pythagorean Theorem - a2 + b2 = c2
Model Problem
Triangle ABC is an isosceles right triangle with BC = 8
A. What AB?
AC?
Do Now: C 8 x A B
Ratio of Hypotenuse : Leg of I.R.T is always
Pythagorean Theorem - a2 + b2 = c2
x2 + x2 = (8)2
2x = 64
x =
x = 32 2 4
Instead of

14. Regents Prep
What is the exact sum of
+ 0

15. Model Problem
The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel?
A = bh
6 in.
600
Draw an altitude of the rhombus. Label x and h as shown x h
6 in.
6 in.
600
Hypotenuse is 2 times the shorter leg
6 = 2x
3 = x
Longer leg is times the shorter leg
A = bh = 6( ) = 31.2 in2
h =

16. Model Problem
A baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does the second baseman throw a ball to home plate?
hypotenuse is times the length of a leg. 2
90’
Isosceles Right Triangle
90’
 90 = ’ 2