1. Special Right Trianglesb A C B a c 45
Consider: Right ΔABC with <A = <B = 45°
Given
Inverse ITT
Pythagorean Theorem
Substitution (2, 3)
Addition
Simplifying Radicals
<A = <B
a = b
c2 = a2 + b2
c2 = a2 + a2
c2 = 2a2
c =

2. 45° - 45° - 90° Triangles
Theorem: In a triangle, the hypotenuse is √2 times as long as a leg
Ex 1) Find x
Ex 2) Find y
Ex 3) Find z m z 12 x y 6

3. Application Questions
Find the length of a diagonal of a square with sides 10 in long.
Find the length of a side of square whose diagonal is 4 cm.
Solve for y:
Solution: 10√2
Solution: 2√2
45° ☐ 6 10 y
Solution: 8√2

4. Consider: Right ΔABC with <A = 30° and <B = 60°☐ B C c a D c a
Consider: Right ΔABC with <A = 30°
and <B = 60° 30 60
<A = 30°, <B = 60
Draw CD s.t. CD = a, AD = c
ΔACD ≅ ΔACB
<D = <B = <DAB = 60°
ΔDAB is equilateral
c = 2a
c2 = a2 + b2
(2a)2 = a2 + b2
4a2 = a2 + b2
b2 = 3a2
b = a√3
Given
Ruler Postulate
SAS
CPCTC
If equiangular then equilateral
Def of equilateral
Pythagorean Theorem
Substitution (6,7)
Multiplication
Subtraction
Square Root Property

5. 30° - 60° - 90° Triangles x 2x
x√3 ☐ 30
Theorem: In a triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.
Ex 1) Find x and y
Ex 2) Find a and b
Ex 3) Find m and n triangle is eqilateral 5 y x 30 b 8 30 60 a m 16 n
m = 8√3
n = 16
x = 10
y = 5√3
a = 4√3
b = 4