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Geometry 1H: Triangle Congruence Unit Review G-CO.7. Learning Target: I can show that two triangles are congruent through rigid motions if and only if the corresponding pairs of sides and corresponding pairs of angles are congruent. 1. Given that ABC A ' B ' C ' is a rotation of Name ______________________________________ Period _______________ Date _________________ G-CO.8. Learning Target: I can explain which series of angles and sides are essential in order to show congruence through rigid motions 2. (a) Given that BD bisects ABC and ADC , explain why BAD BCD . ____________________________________ ____________________________________ ____________________________________ (b) If mA 75 and mADC 45 , find the measurement of ABC . (a) Are the two triangles congruent? ______ (b) Explain why or why not. ____________________________________ ____________________________________ ____________________________________ 2. Using the diagram below, describe one way to map ABE onto CDE . mABC = ______________ 3. What additional information would you need to prove that the two triangles shown are congruent? ________________________ ______________________________________ If mA (3x 5) and mC (5 x 17) : Find the value of x. _________ Find mA _____________ Geometry 1: Triangle Unit Test REVIEW 6/6/16 PUHSD Geometry Curriculum Team Page 1 of 5 G-CO.9. Learning Target: I can prove the following theorem in narrative paragraphs, flow diagrams, in two column format, and/or using diagrams without words: points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. I can make the following formal constructions using a variety of tools: constructing perpendicular bisectors. 5. Given the following segment AB , construct its perpendicular bisector. Label your bisector HG . Label a point M anywhere on HG such that M is NOT at the intersection of AB and HG . 4. Given the following diagram, fill in the reasons for the following proof. Given: PM is the perpendicular bisector of XY Prove: PX PY (b). Using your construction, explain why point M is equidistant from A and B. Statements Reasons _______________________________________ 1. PM is the perpendicular bisector of XY 1. _______________________________________ 2. XM YM 2. 3. PMX PMY 3. 4. PM PM 4. 5. PMX PMY 6. PX PY _______________________________________ _______________________________________ 5. 6. Geometry 1H: Triangle Unit REVIEW 6/6/16 PUHSD Geometry Curriculum Team Page 2 of 5 G-CO.10. Learning Target: I can prove the following theorems in narrative paragraphs, flow diagrams, in two-column format, and/or using diagrams without words: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the medians of a triangle meet at a point. 7. Given acute scalene triangle, construct the medians. ABC, 6. Given the following isosceles triangle, explain the theorem that “if two sides of a triangle are congruent, then the angles opposite those sides are congruent.” (b) Using your construction, define a centroid and explain its characteristics. _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ 8. Given the triangle shown below. 6. Given the triangle below, find the value of x and the measurement of each angle. (a) What type of triangle is this? _________________ A B C (b) List 2 properties for this type of triangle. _______________________________________ 1 _______________________________________ (c) Find the value of x. _______ Geometry 1H: Triangle Unit REVIEW 6/6/16 PUHSD Geometry Curriculum Team Page 3 of 5 G.CO-13. Learning Target: I can make the following formal constructions using a variety of tools: an equilateral triangle inscribed in a circle. 11. Use the diagram below to answer the following questions. 9. Construct an equilateral triangle inscribed in a circle. Leave all your construction marks. Part A: Are the two triangles congruent? If so, state how. If not, what additional information do you need? Part B: Is KJL LMK ? How do you know? G-SRT.5. Learning Target: I can prove relationships in geometric figures using congruence criteria for triangles. Part C: If mMLK = (7x + 4)° and mJKL = (5x + 30)°, what is the value of x? 10. If ABC CDA , which of the following must be true? (Circle all that apply.) a. AB CA Part D: What is the mMLK ? b. BC DA c. CAB ACD d. ABC CAD Part E: If mMKL is 21°, what is the measure of KML ? Part F: What is the measure of JLK ? Geometry 1H: Triangle Unit REVIEW 6/6/16 PUHSD Geometry Curriculum Team Page 4 of 5 G-SRT.8. Learning Target: I can solve real world problems involving right triangles using the Pythagorean Theorem. 12. In a computer catalog, a computer monitor is listed as being 19 inches. This is the diagonal distance across the screen. The screen itself measures 10 inches in height. (a) What is the length of the screen? (b) If companies price monitors by the foot, how many feet is the monitor long? (c) If a company were to charge by the length of the monitor, how much would this monitor cost for $75.50/foot? Geometry 1H: Triangle Unit REVIEW 6/6/16 PUHSD Geometry Curriculum Team Page 5 of 5