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Mathematics 8 Items to Support Formative Assessment Unit 2: Geometry 8.G.A. Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. 8.G.A.5 Task Examine the diagram below, where line a line b and line c is a transversal. Determine the relationship between Ð1 and Ð7 . Justify your reasoning using what you know about the angle relationships when a set of parallel lines is cut by a transversal. Sample Answer: Angle 5 and angle 7 form a linear pair, which means they are supplementary. Angle 1 and angle 5 are corresponding angles and since line a is parallel to line b, the corresponding angles are congruent. Therefore, angle 1 and angle 7 must be supplementary. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 8.G.A.5 Item Using the diagram below, determine if each given angle pair is congruent or supplementary. Mark your answer by selecting the appropriate box. A. 2 & 8 B. 4 & 6 C. 3 & 6 D. 1 & 5 E. 2 & 7 Congruent Congruent Congruent Congruent Congruent Supplementary Supplementary Supplementary Supplementary Supplementary Answer: A. B. C. D. E. Congruent – alternate exterior angles Congruent – alternate interior angles Supplementary – consecutive interior angles Congruent - corresponding Supplementary – 1 and 2 are supplementary, 1 and 7 are congruent, therefore 2 and 7 are supplementary by substitution. 8.G.A.5 Item Using the diagram below, select if the given angle is congruent to 4. Mark your answer by selecting the appropriate box. A. 2 B. 5 C. 6 D. 8 E. 3 F. 1 Yes, congruent Yes, congruent Yes, congruent Yes, congruent Yes, congruent Yes, congruent Not congruent Not congruent Not congruent Not congruent Not congruent Not congruent Answer: A. B. C. D. E. F. No, supplementary because they form a straight angle No, supplementary because they are consecutive interior angles Yes, congruent because they are alternate interior angles Yes, congruent because they are corresponding angles No, supplementary because they form a straight angle Yes, congruent because they are vertical angles. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 8.G.A.5 Item The angle measures of a triangle are 2x, 3x, and 5x. Circle every angle measure in the triangle. A. B. C. D. E. F. G. H. 9 18 27 30 36 45 54 90 Answer: E, G, H 2x + 3x + 5x = 180 10x = 180 x = 18 2(18) = 36 3(18) = 54 5(18) = 90 8.G.A.5 Item Using the figure below, find the value of a, b, and c. Answer: Use exterior angle theorem to solve for x 130 = 8x + 2x x = 13 a = 50 (130 – 50) b = 76 (180 – (8)(13)) c = 154 (180 –(2)(13)) Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 8.G.A.5 Item Use the diagram below to determine the following, given . a. Find the m Ð ACB = ___________ and explain your reasoning. b. Find the m Ð B = ___________ and explain your reasoning. c. Find the m Ð E = ___________ and explain your reasoning. d. Find the m Ð A = ___________ and explain your reasoning. e. What can you conclude about DABC and DEDC ? Justify your reasoning. Answers: a. Since ÐDCE and ÐACB are vertical angles and all vertical angles are congruent, mÐACB = 54 0 . b. ÐD and ÐB are alternate interior angles. If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Therefore, ÐD @ ÐB and mÐB = 65 0 . c. The sum the interior angles of a triangle is 180 degrees. The sum of angle D and angle DCE is 1190. Then, I subtracted 1800-1190, which equals 610. Therefore, the mÐE = 610 . d. ÐA and ÐE are alternate interior angles. If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Therefore, ÐA @ ÐE and mÐA = 610 . e. DABC and DEDC are similar triangles, since at least two pairs of corresponding angles are congruent. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 8.G.A.5 Item Gables are the triangles formed by the slope of the roof in the front of a home. The angles of the gables are labeled below. A B C Y X Z Angle A is congruent to angle X and angle B and angle Y are right angles. What can you deduce about ΔABC and ΔXYZ? Sample Answer: If two angles of one triangle are congruent to two corresponding angles in another triangle, then the triangles are similar. Since all right angles are congruent, angle B is congruent to angle Y. Therefore, since angle A is congruent to angle X and angle B is congruent to angle Y, ΔABC must be similar to ΔXYZ. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.