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Name September 29, 2016 Math 2 quiz review assignment page 1 Geometric proofs: recap and practice At our next class on Friday 9/30, we will have a half-period quiz on geometric proof. Review outline: what we have so far Proof writing styles and strategies two-column proofs, flowchart proofs, and paragraph proofs turning statements into if-then statements, identify what’s given and what’s to be proved Facts (definitions) all the definitions of commonly used geometry to date (see handout) o angle bisector, median, altitude, perpendicular bisector, midpoint, square, perpendicular, supplementary, straight angle, bisect, isosceles, equilateral, equiangular, rhombus, congruence (CPCTC), Rotation around a point is 360 and so on. Facts we’ve assumed (postulates) many algebra properties and rules o addition property, subtraction property, reflexive property, transitive property, substitution property Angle Addition Segment Addition triangle congruence methods: SSS, SAS, ASA, AAS, HL Facts we’ve proved (theorems) Vertical Angle Theorem Perpendicular Bisector Theorem and its converse (PBT and CPBT) Isosceles Triangle Theorem and its converse (ITT and CITT) Equilateral triangles must be equiangular; equiangular triangles must be equilateral. Supplements of congruent angles are congruent Congruent, supplementary angles are equal to 90 Skills needed for the quiz: drawing and marking a diagram with the given information writing a converse of a statement idenitfy the given and prove from a general statement and make it specific to a daigram write clear and convincing arguments in any of the styles studied o write triangle congruence proofs o use triangle congruence as a step towards proving other things o applying ITT and CITT as well as PBT and CPBT Name September 29, 2016 Math 2 quiz review assignment page 2 Practice problems 1. Given: bisects Prove: is a median. . is isosceles Complete this proof without using the reflexive property in your proof. 2. Read the paragraph proof below and edit it. There are errors to correct. You may state the errors and the corrections in list form, or you can rewrite the proof correctly in any form you like. B Given: Prove: , A C E D Because , , by SSS. Since the large triangles are congruent their corresponding parts are congruent. Also, because it is the same side. So by SAS; therefore by CPCTC. Name September 29, 2016 3. Math 2 quiz review assignment page 3 G Given: A is the midpoint of FG A 3 1 Ð1@ Ð3 AB @ AC F 2 Prove: BF @ CG B 4. Given: AED is the bisector of C A Prove: E B D C Name September 29, 2016 5. Math 2 quiz review assignment page 4 Consider the statement: The medians of congruent triangles are congruent. a. Write the statement in if-then form. b. Create a labeled diagram that illustrates the given situation c. Write given and prove statements that refer specifically to your labeled diagram (i.e. using the letters you have chosen etc.) d. Write the proof. Name September 29, 2016 6. Given: A 2 1 C Prove: AB CD Math 2 quiz review assignment page 5 A 7. Given: X Y Prove: Z C B