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Transcript
Worksheet 5.05 Name:______________________________ In problems 1 - 4, select the correct multiple choice response. 1. In the figure ABC is a right triangle A Assume temporarily that mC > 90°. It follows that mC + mB > 180°. This contradicts the triangle sum theorem that states the sum of all 3 angles in a triangle sums to 180°. What conclusion can be drawn from this contradiction? a. ABC is a not right triangle b. mC > 90° c. mC d. mB 90° 90° In problems 11 – 13, select the correct multiple choice response. 2. In the figure LMP is an isosceles triangle with LM LP Let us assume that M C B L P . Then it follows that LM LP since if angles aren’t congruent then sides opposite aren’t congruent. What conclusion can be drawn from this contradiction? M P P a. M P b. M c. LM d. LMP is not an isosceles triangle LP K 3. In the figure mL = 70° and mK = 45° 45° 70° 1 L D Assume temporarily that m 1 115°. Then it follows that mL and mK cannot be 70° and 45° since this contradicts the Exterior Angle Theorem that states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. What conclusion can be drawn from this? a. mL 70° b. m 1 = 115° c. mK 45° d. The exterior angle theorem is false. t 1 4. In the figure, m 1 = 110° and m 2 = 110° p m 2 Let us assume that line p is not parallel to line m. Then it follows that m 1 and m 2 cannot each be 110° since this contradicts the Alternate Exterior Angles Converse Theorem that states that if two lines are cut by a transversal so that alternate exterior angles are congruent then the lines must be parallel. What conclusion can be drawn from this? a. line p is parallel to line m b. m 1 110° c. m 2 110° d. line p is not parallel to line m