1. Bell Ringer 12-7-17 1. What are special right triangles?
2. What are the rules for a triangle?
3. What are the rules for a triangle?

2. Special Right Triangles (review from Math II)
Thursday, December 7, 2017

3. Special right triangles
and are Special Right Triangles.
A triangle has angles in a ratio.
A triangle has angles in a ratio.
Because of these angle ratios, the sides have special rules….
See information in chapter 9.4 in the Geometry book (p ).

4. 45-45-90 Leg = x Hypotenuse = x√2
A triangle is also called an Isosceles Right Triangle.
This triangle has a hypotenuse and congruent legs.
The hypotenuse is the leg times the square root of 2.
Leg = x
Hypotenuse = x√2

5. 30-60-90 Short Leg = x Long Leg = x√3 Hypotenuse = 2x
This triangle has a hypotenuse, a long leg, and a short leg.
We know the longest sides of a triangle are across from the biggest angle and the shortest are across from the smallest angle, so the short leg is across from the 30° angle and the long leg is across from the 60° angle.
Short Leg = x
Long Leg = x√3
Hypotenuse = 2x

6. examples
The rule is the hypotenuse is the leg times the square root of 2, so x = 8√2.
The rule is the hypotenuse is twice the short leg, so y = 16.
The rule is the long leg is the short leg times the square root of 3, so x = 8√3.

7. Assignments Classwork: Geometry book p.554-555 #12-29 all
Homework: Trigonometry Prerequisite: Special Right Triangles

8. Exit Ticket
1. Which special right triangle is also known as an isosceles right triangle?
2. In a , how does the short leg relate to the long leg?
3. In a , how do the legs relate to the hypotenuse?