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Triangles, Multiple, & Oddball Figures

Triangles, Multiple, & Oddball Figures. Triangle Facts. The sum of the angle measures in a triangle is always 180° The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles . In any triangle

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Triangles, Multiple, & Oddball Figures

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  1. Triangles, Multiple, & Oddball Figures

  2. Triangle Facts • The sum of the angle measures in a triangle is always 180° • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. • In any triangle • The longest side is opposite the largest angle • The shortest side is opposite the smallest angle • The area of a triangle is given by A = (1/2)bh, where b is the base and h is the height.

  3. Equilateral Triangles • All interior angles are 60°, and all sides are the same length 60° Isosceles Triangles 60° 60° • Two sides are the same length, and the angles facing those sides are equal.

  4. Right Triangles • Right Triangles contain a 90° angle. The sides that form the 90° angle is the hypotenuse. The sides are related by the Pythagorean theorem a2+b2=c2, where a and b are the lengths of the legs, and c is the length of the hypotenuse c a2+b2=c2 a b

  5. “Special” Right Triangles • Special triangles are right triangles whose side lengths always come in predictable ratios • Common Right Triangles • 3x:4x:5x • ie: 6:8:10 • 32 + 42 = 52? • 9 + 16 = 25 • 25 = 25 • 5:12:13 • 52 + 122 = 132? • 25 + 144 = 169 • 169 = 169 • What are some other Special Right Triangles

  6. “Special” Right Triangles

  7. 45°- 45°- 90° Right (Isosceles) Triangles • Side length ratios of 1:1:√2. An isosceles right triangle is formed when a square is divided in half by one of its diagonals. √2 1 30°- 60°- 90° Right Triangles 1 • Side length ratios of 1:√3:2. When an equilateral triangle is divided in half, the result is a 30-60-90 triangle. 2 1 √3

  8. The Kaplan Approach to Multiple and Oddball Figures • You may see a combination of geometric shapes or an oddball figure on the GRE • These problems are intended to look difficult but can often be simplified into familiar geometric shapes such as: • Special Right Triangles • Rectangles or Squares • Circles

  9. Examples • Can you identify multiple shapes for the following examples? • Now, turn to page 207 in your textbook and solve the given problem. When you have found the correct answer, move on to page 208.

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