1. GHSGT Review
Triangles and Circles

2. Scalene Triangles
A scalene triangle has NO equal sides and NO equal angles
The longest side is across from the largest angle, and the shortest across from the smallest
70⁰
10 cm cm
80⁰ 30⁰
12 cm

3. Isosceles Triangles All isosceles triangles have two equal sides
The two angles across from those sides are equal to each other also
30⁰
7 cm cm
75⁰ ⁰
4 cm

4. Equilateral Triangles
Equilateral means equal-sided: all three sides are equal
Equilateral triangles also have three angles that are all equal (equiangular)
Each angle measures 60⁰ because 180⁰ divided into three equal angles is 60⁰ each.
60⁰
10 cm 10 cm
10 cm
60⁰ 60⁰

5. Right Triangles
A right triangle can be either scalene or isosceles, based on the leg lengths
Every right triangle has two legs and a hypotenuse; the hypotenuse is always the longest side, and it’s across from the right angle
45⁰
67⁰
33⁰
5 cm 13 cm
12 cm
8 cm cm
8 cm

6. The Pythagorean Theorem
The Pythagorean Theorem only works for right triangles; it can find the length of a missing side
Use , where a and b can be either leg, but c must be the hypotenuse length
(9)² + (12)² = (x)²
= x²
= x²
15 cm = x
9 cm x
12 cm

7. Another Pythagorean Example
Sometimes you need to cancel with the Pythagorean Theorem
(10)² + (x)² = (26)²
x² = 576
x² = 476
x = 24 in
10 in 26 in x

8. Central Angles
When diameters or radii are drawn in a circle, they form central angles
The sum of the central angles of a circle is 360⁰
A semicircle (half-circle) would be 180⁰
This angle would measure 123⁰ because = 237, and 360 – 237 = 123 degrees left over from the circle
180⁰ ⁰

9. 1. In this drawing, the length of side A equals 24 inches
1. In this drawing, the length of side A equals 24 inches. The length of side C is 26 inches. Which formula would determine the length of side B? A. B. C. D.
A C
24 in in B

10. 2. Beth wants to make a design with a circle divided into pie-shaped pieces of equal size. What is the smallest number of pieces Beth can have if she wants the central angles to be right angles?
A. 2
B. 3
C. 4
D. 5

11. 3. A triangle has side lengths 6, 12, and 12
3. A triangle has side lengths 6, 12, and 12. What type of triangle is it?
A. equilateral
B. isosceles
C. right
D. scalene

12. Solutions
1. D – to most easily determine the length of side B, you would subtract those squares and then find the square root
2. C – Beth’s design would have pieces that are ¼ of the circle
3. B – Two equal lengths would mean the triangle is isosceles