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GHSGT Review Triangles and Circles
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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