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8-1 through 8-2 Vocabulary

Name: ___________________________________
Date: _________________________
Block: ______________
Across
(p. 556) Notice that a rectangular _____ is used to show perspective.
(p. 550) You can also use side lengths to ________ a triangle as acute or obtuse.
(p. 548) A Pythagorean ______ is a set of three nonzero whole numbers a, b, and c, such that a² + b² = c².
(p. 537) These three right triangles share a(n) _______ relationship.
(p. 549) A right triangle with side ______ 3, 4, and 5 is called a 3-4-5 right triangle.
(p. 550) If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is a(n) ______ triangle.
(p. 550) You can use this theorem to help you determine whether a triangle is a right triangle given the ________ of all three sides.
(p. 548) You can use the Pythagorean Theorem to find the measure of any side of a(n) _____ triangle given the lengths of the other two sides.
(p. 547) The ___________ Theorem is perhaps one of the most famous theorems in mathematics.
(p. 548) If the measures of the sides of any right triangle are not _____ numbers, the measures do not form a Pythagorean triple.
(p. 538) ________ (of a triangle) - a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side
(p. 537) In a right triangle, an altitude drawn from the ______ of the right angle to the hypotenuse forms two additional right triangles.
(p. 551) Triangle ___________ Theorem - The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
(p. 539) The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of a(n) ___ of this triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that ___.
(p. 547) It relates the lengths of the hypotenuse (side opposite the right angle) and legs (sides ________ to the right angle) of a right triangle.
(p. 556) A point in space is represented by a(n) _______ triple of real numbers (x, y, z).
(p. 548) When finding the length of a side using the Pythagorean Theorem, use only the ________ and not the negative square root, since length cannot be negative.
Down
(p. 547) In a right triangle, the sum of the ______s of the lengths of the legs is equal to the ______ of the length of the hypotenuse.
(p. 550) If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is a(n) _______ triangle.
(p. 550) If the sum of the squares of the lengths of the ________ sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle.
(p. 547) It relates the lengths of the hypotenuse (side ________ the right angle) and legs (sides adjacent to the right angle) of a right triangle.
(p. 549) Since the hypotenuse of a right triangle is always the _______ side, the length of the ladder in Example 3 must be greater than 5 or 12 feet. Since 7 and 11 feet are both less than 12 feet, choices A and B can be eliminated.
(p. 548) One _______ Pythagorean triple is 3, 4, 5; that is, the sides of a right triangle are in the _____ 3:4:5.
(p. 537) When the means of a proportion are the same number, that number is called the _________ mean.
(p. 539) The altitude drawn to the ___________ of a right triangle separates the __________ into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.
(p. 550) The ________ of the Pythagorean Theorem also holds.
(p. 550) If the measures of any of the sides of a triangle are expressed as ________, you may wish to use a calculator to determine which length is the longest.
(p. 538) By the definition of _______ polygons, you can write the following proportions comparing the side lengths of these triangles.
(p. 538) ________ing Triangles - To reorient the right triangles in Example 2, first match up the right angles. Then match up the shorter sides.
(p. 547) The geometric mean can be used to prove the Pythagorean _______.
(p. 537) The geometric ____ between two numbers is the positive square root of their product.