GHSGT Review Triangles and Circles

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 15 cm 80⁰ 30⁰ 12 cm

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 7 cm 75⁰ 75⁰ 4 cm

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

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 11.3 cm 8 cm

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 81 + 144 = x² 225 = x² 15 cm = x 9 cm x 12 cm

Another Pythagorean Example Sometimes you need to cancel with the Pythagorean Theorem (10)² + (x)² = (26)² 100 + x² = 576 -100 -100 x² = 476 x = 24 in 10 in 26 in x

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 180 + 57 = 237, and 360 – 237 = 123 degrees left over from the circle 180⁰ 57⁰

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 26 in B

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

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

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