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Lessons 5-3 through 5-5 Vocabulary

Name: ___________________________________
Date: _______________________ Block: _______
Across
(p. 345) If two sides of a triangle are congruent, or the triangle is _________, then the angles opposite those sides are congruent.
(p. 346) Be careful to write the symbols correctly in situations where ____ are used.
(p. 345) The measure of an exterior angle of a triangle is greater than the measure of _______ its corresponding remote interior angles.
(p. 344) ___________ Property of Inequality - 1. If a > b, then a - c > b - c. 2. If a < b, then a - c < b - c.
(p. 355) By showing this assumption to be logically impossible, you prove your assumption false and the original conditional true. Sometimes this is called proof by _________.
(p. 353) ______ logic uses a rectangular array in which you record what you have learned from clues in order to solve a logic or reasoning problem.
(p. 355) The proofs you have written have been ______ proofs--you started with a true hypothesis and proved that the conclusion was true.
(p. 365) You can use the Triangle Inequality Theorem to determine the range of ________ lengths for the third side.
(p. 345) The sides that _____ the angle cannot be the sides opposite the angle.
(p. 364) To show that it is not possible to form a triangle with three side lengths, you need only show that one of the three triangle inequalities is not ____.
(p. 355) In an indirect or proof by ______________, you temporarily assume that what you are trying to prove is false.
(p. 344) __________ Property of Inequality - a < b, a = b, or a > b.
(p. 346) If one angle of a triangle has a(n) _________ measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
(p. 355) By showing this assumption to be logically impossible, you prove your assumption _____ and the original conditional true.
(p. 345) Be careful to correctly identify the side ________ an angle.
(p. 345) Each exterior angle of a triangle has two ______ interior angles that are not adjacent to the exterior angle.
(p. 364) The ___ of the lengths of any two sides of a triangle must be greater than the length of the third side.
(p. 344) ________ Property of Inequality - 1. If a > b, then a + c > b + c. 2. If a < b, then a + c < b + c.
(p. 357) You can represent an even number with the expression 2k and a(n) ___ number with the expression 2k + 1 for any integer k.
(p. 364) While a triangle is formed by three segments, a(n) _______ relationship must exist among the lengths of the segments in order for them to form a triangle.
(p. 345) The ________ side and largest angle of △ABC are opposite each other.
Down
(p. 344) Definition of __________ - For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c.
(p. 357) You can represent an ____ number with the expression 2k.
(p. 365) The compound inequality 4 < x < 10 is read x is ______ 4 and 10.
(p. 357) Indirect proofs are often used to prove concepts in ______ theory.
(p. 344) __________ Property of Inequality - 1. If a < b and b < c, then a < c. 2. If a > b and b > c, then a > c.
(p. 356) _____________ - Everyday use - an inconsistency or discrepancy; Math meaning - a principle of logic stating that an assumption cannot be A and the opposite of A at the same time.
(p. 345) The shortest side and ________ are opposite each other.
(p. 344) The definition of inequality and the properties of inequalities can be applied to the ________ of angles and segments, since these are real numbers.
(p. 346) If one side of a triangle is ______ than another side, then the angle opposite the _______ side has a greater measure than the angle opposite the shorter side.
(p. 346) The side-angle relationships in an obtuse _______ triangle are true for all triangles, and are stated using inequalities in the theorems below.
(p. 356) Indirect proofs can be used to prove _________ concepts.
(p. 356) Indirect reasoning and proof can be used in ________ situations.
(p. 355) In a(n) ________ proof or proof by contradiction, you temporarily assume that what you are trying to prove is false.
(p. 346) The ______ for angle (∠) looks similar to the symbol for less than (<), especially when handwritten.
(p. 365) When the lengths of two sides of a triangle are known, the third side can be ___ length in a range of values.