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### 21 Cards in this Set

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 What is the sum of the interior angles of any triangle? 180 degrees. What is a scalene triangle? What is the relationship between the 3 angles in a scalene triangle? A scalene triange has 3 sides of different lengths. The 3 angles are unequal. What is an isosceles triangle? What is the relationship between the sides and the angles of an isosceles triangle? An isosceles triangle has 2 equal sides and 2 equal angles. The equal sides are opposite the equal angles. What is an equilateral triangle? What is the measure of every angle of an equilateral triangle? An equilateral triangle has 3 equal sides. Every angle of an equilateral triangle measures 60 degrees. What is a right triangle? What are the 3 sides of a right triangle called? A right triangle has one 90 degree angle. The 2 perpendicular sides (shortest dies) are called the legs, while the longest side of the triangle, opposite the right angle, is called the hypoteneuse. What is the relationship between the lengths of the 3 sides of a right triangle? The right triangle's sides are related by the Pythagorean theorem: a²+b²= c² where a and b are the lengths of the triangle's legs and c is the length of the hypoteneuse. What are Pythagorean triplets? What are the most common Pythagorean triplets? Pythagorean triplets are right triangles whose sides have INTEGER lengths. The most common one is the 3-4-5 triangle. Other common ones are multiples of 3-4-5 (such as 6-8-10), 5-12-13 and 7-24-25. What is the formula for the area of a triangle? A=½bh where b is the base and h is the height. In order to find the height, it may be necessary to drop a perpendicular from a point to a side. What is an exterior angle of a triangle? How can you calculate it? An exterior angle is an angle formed by extending one of the sides of the triangle past the vertex. The measure of an exterior angle equals the sum of the measures of the two nonadjacent interior angles. What is the relationship between the 3 sides of any triangle? The length of any side of a triangle must be greater than the difference between the lengths of the other two sides AND less than their sum. In other words, for any side C, a-b  c  a+b. What is the relationship between the sides of a 30-60-90 triangle? If the length of the smaller leg is x, the larger leg measures xã3 (x times square root of 3) and the hypoteneuse is 2x. What is the relationship between the sides of a 45-45-90 triangle? If the 2 legs are each x, the hypoteneuse is xã2 (x times square root of 2). What happens if you drop an altitude to a side of a right triangle? When an altitude in a right triangle is drawn, 3 similar triangles are created with proportional lengths (the original triangle and the 2 new triangles). What is the relationship between the sides and the angles of any triangle? In any triangle, the largest side is opposite the largest angle and the smallest side is opposite the smallest angle. What is a rectangle? What is true about opposite sides of a rectangle? What is true about the diagonals? What is the formula for the perimeter? What is the formula for the area? A rectangle is a quadrilateral with 4 right angles. Opposite sides are parallel. The diagonals are equal in length and divide each other in half. The perimeter P = 2l + 2w. The area A = l x w. What is a square? What is the perimeter of a square? What is the area of a square? A square is a rectangle with 4 equal sides. The perimeter p = 4s. The area A = s². What is a parallelogram. Are rectangles and squares parallellograms? What is the perimeter? What is the area? A parallelogram is a quadrilateral in which opposite sides are parallel. Rectangles and square are parallelograms that happen to have 90 degree angles. The perimeter P is the sum of the sides. The area A = b x h. The height h is formed by dropping an altitude (as in a triangle). What is the relationship between the sides of a 30-60-90 triangle? If the length of the smaller leg is x, the larger leg measures xã3 (x times square root of 3) and the hypoteneuse is 2x. What is a trapezoid? What is the perimeter? What is the area? A trapezoid is a quadrilateral with 2 parallel sides and 2 sides that aren't parallel. The 2 parallel sides are considered the bases. The perimeter is the sum of its sides. The area A = ½h(b1 + b2) where h is the height and b1 and b2 are the bases. What is a rhombus? Is a square a rhombus? What is the perimeter of a rhombus? What is the area? A rhombus is a parallelogram with 4 equal sides. A square IS a rhombus that has 90 degree angles. The perimeter of a rhombus p = 4s. The area of a rhombus A = bh. What is a regular polygon? What is the 5-sided polygon? What is a 6-sided polygon? What is an 8-sided polygon? What do the interior angles of any polygon add up to? A regular polygon is a figure with sides that are all of equal length. A 5-sided polygon is a PENTAGON. A 6-sided polygon is a HEXAGON. An 8-sided polygon is an OCTAGON. The sum of the angles of a polygon with n sides = (n-2) x 180. For example, the sum of the angles of a quadrilateral is 360 and the sum of the angles of a pentagon is 540.