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Geometry with Measurement Chapter 2 Review Key Name:___________________ Date:______ Period:___ Use inductive reasoning to describe each pattern and find the next two terms of each sequence. 1. 1, 8, 27, 64, 125… pattern: # cubed next two: 216, 343 2. 0, 1, 1, 2, 3, 5, 8, 13… pattern: add new # to previous next two: 21, 34 Write the converse, inverse, and contrapositive for each statement. Determine the truth value for each (either true or false). Give counter example for any FALSE statements. 3. If two angles are a vertical pair then the two angles are congruent. converse If two angles are congruent then the angles are a vertical pair. truth value false counter example __40 40 angles equal but don’t form an X. inverse If two angles are not a vertical pair then the angles are not congruent. truth value false counter example see above example contrapositive If two angles are not congruent then the angles are not a vertical pair. truth value true. counter example __________________________________________________________ 4. If Jerrod is in 11th grade, then Jerrod is in high school. converse – If Jerrod is in high school, then he is in the 11th grade. truth value false counterexample Could be in the 9th, 10th, or 11th grade. inverse - If Jerrod is in high school, then he is in the 11th grade. truth value false counterexample Could be in the 9th, 10th, or 11th grade. contrapositive If Jerrod is in high school, then he is in the 11th grade truth value true counterexample ___________________________________________________________ Matching: Refer to the figure on the right for #5 – 7. 5.) __A____ Linear pair A) 4 & 5 6.) ___C___ Complementary angles B) 3 & 5 7.) ___B___ Vertical angles C) 1 & 2 Name the property that justifies each statement. 8. mABC = mDEF and mDEF = mABC Symmetric 9. AB = CD, CD = EF. Therefore, AB = EF. Transitive 10. If x + 7 = 10, then x = 3. Subtraction 11. If AB + 12 = 25, then 12 = 25 – AB. Subtraction 12.. A A Reflexive 13. Reasoning Use the diagram at the right to complete the proof below. Statements B LACB & LBCE supplementary A. mLACB + mLBCE = 180 B. 5x + 9x + 40 = 180 C. 14x + 40 = 180 D. 14x = 140 E. x = 10 F. mLBCE = 9(10) + 40 = 130 G. LBCE ACD H. mLACD = 130 Reasons Given A. Definition of Supplementary B. Substitution C. Combine like terms D. Subtraction E. Division Property of Equality F. Substitution Property G. Vertical Angles are = H. Substitution Property 14. Find the value of x. 15. Use your work from #14 to complete a two-column proof with statements and reasons for each step. D E 5x 4x A B C <ABE + <EBD = 90 Definition Complementary 4x + 5x = 90 9x = 90 X = 10 Substitution Combine like terms Division 16. a) Write an equation and solve for x. b) Find the measure of each angle. mAEB _______ mBEC _______ mCED _______ mAED _______ 17. Use your work from #16 to complete a two- column proof with statements and reasons for each step. < BEA = <CED 3x + 60 = 5x – 6 60 = 2x – 6 66 = 2x 33 = x Vertical Angles are congruent Substitution Subtraction Addition Division