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8: Q4 Topic Proficiency Scale Domain: Geometry Topic: Angles 4.0 Going Beyond I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. I know all of the Simple and Complex Learning Goals. 3.0 Complex Goals Grade Level Target C1: Use informal arguments to establish facts about the angles created when 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. parallel lines are cut by a transversal. (8.G.5) C2: Use informal arguments to establish facts about the angle sum and exterior angles of triangles and about the Angle-Angle Criterion for similarity of triangles. (8.G.5) I know all of the Simple Learning Goals. 2.0 Simple Goals Academic Vocabulary: V1: Angle-Angle Criterion (AA Criterion) V2: exterior angles V3: interior angles V4: transversal S1: Know facts about the angles created when parallel lines are cut by a transversal. S2: Know facts about angle sum and exterior angles of triangles and the angleangle criterion for similarity of triangles. 1.5 1 0.5 0 I know all but one of the Simple Learning Goals. I know some of the Simple Learning Goals. I know only one of the Simple Learning Goals. No evidence of knowing the Learning Goals. ©Farmington Municipal Schools - 8th grade NMCCSS Math Revised May, 2016 8: Q4 Teacher Resources Geometry (G): Angles Understand congruence and similarity using physical models, transparencies, or geometry software. Standards Mathema,cal Agile Mind Explana,ons and Examples Students are Prac,ces expected to: 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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Connec=ons: 6-‐8.WHST.2b,f; 6-‐8.WHST.1b; ET08-‐S6C1-‐03; ET08-‐S1C1-‐01; ET08-‐S1C3-‐03 8.MP.3. Construct viable arguments and cri=que the reasoning of others. Topic 14: Exploring Geometric Rela=onships. Students can informally prove rela=onships with transversals. Example: Show that m! + m! + m! = 180˚ if l and m are parallel lines and t1 & t2 are transversals. ! + ! + ! = 180˚. Angle 1 and Angle 5 are congruent because • they are corresponding angles (! 8.MP.4. Model with mathema=cs. ! 8.MP.6. ACend to precision. Therefore m! ). ! can be subs=tuted for . ! because alternate interior angles are congruent. ! can be subs=tuted for! + m! . + m! = 180˚ ! Students can informally conclude that the sum of a triangle is 180o (the angle-‐ sum theorem) by applying their understanding of lines and alternate interior angles. Examples: • In the figure below, line x is parallel to line yz: ! • Angle a is 35 o because it alternates with the angle inside the triangle that measures 35 o. Angle c is 80 o because it alternates with the angle inside the triangle that measures 80 o. Because lines have a measure of 180 o, and angles a + b + c form a straight line, then angle b must be 65 o (180 – 35 + 80 = 65). Therefore, the sum of the angles of the triangle are 35 o + 65 o + 80 o. ©Farmington Municipal Schools - 8th grade NMCCSS Math Revised May, 2016