# MTH 2010 Week 2: Assignment 4 answer the following questions 1. Prove that, if two triangles ABC and RST are congruent to the same triangle XYZ, then they are congruent

MTH 2010 Week 2: Assignment 4 answer the following questions 1. Prove that, if two triangles ABC and RST are congruent to the same triangle XYZ, then they are congruent to each other. 2. Referring to the diagram, name all pairs of; a. Alternate interior angles b. Corresponding angles c. Alternate exterior angles a b e f c d g h 3. Form the converse of each of the following statements. State whether the converse is true or false. a) If I live in New York, then I live in United States b) If two angles are congruent, then the angles are equal in measure c) If two angles are vertical angles, then they are congruent d) If two angles are adjacent, then they have the same vertex. e) If two angles are complementary, then the sum of their measures is 90. f) If two lines are perpendicular to the same line, then they are parallel. 4. Two parallel lines are cut by a transversal. Find the measures of the angles if a pair of interior angles on the same side of the transversal: a) are represented by (5x-32)q and (x + 8)q. b) Have measures such that one angle is 4 times the measure of the other. 5. Prove that, if two lines are parallel to a third line, then the lines are parallel to each other. 6. Given: AX || CY BA bisects CAX, A X BC bisects ACY. Prove: B is a right angle. B C Y 7. Given: BMAAC , M is the midpoint of AC . B Prove: ‘ABM # ‘CBM. A M C 8. You are given the following diagram: J E 1 2 K V L T Given JKAKT, ETAKT, 1 # 2, KL # TV. Prove: ‘JKL # ‘ETV