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GHSGT Review

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.

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GHSGT Review

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  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 15 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 7 cm 75⁰ 75⁰ 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 45⁰ 45⁰ 67⁰ 33⁰ 5 cm 13 cm 12 cm 8 cm 11.3 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 81 + 144 = x² 225 = 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)² 100 + x² = 576 -100 -100 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 180 + 57 = 237, and 360 – 237 = 123 degrees left over from the circle 180⁰ 57⁰

  9. 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

  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. 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

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