Int. Geometry Unit 2 Quiz Review (Lessons 1-4) 1

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1 Int. Geometry Unit Quiz Review (Lessons -4) Match the examples on the left with each property, definition, postulate, and theorem on the left PROPRTIS:. ddition Property of = a. GH = GH. Subtraction Property of = b. If, then c. If = and =, then. Multiplication Property of = + = + 4. ivision Property of = d. If and, then 5. istribution Property of = e. If m = 60, then m = 0 f. If = 0, then = Substitution Property of = 7. Reflexive Property of = g. x+ 6= ( x+ ) 8. Symmetric Property of = h. If m = m, then m = m i. If = and =, then 9. Transitive Property of = = 0. Reflexive Property of ongruence j. If + = +, then =. Symmetric Property of ongruence k. l. If m + m = 90 and m = m,. Transitive Property of ongruence then m + m = 90 FINITIONS:. efinition of ngle isector 4. efinition of Midpoint 5. efinition of Segment isector 6. efinition of ongruent ngles 7. efinition of ongruent Segments 8. efinition of Right ngles 9. efinition of cute ngles 0. efinition of Obtuse ngles. efinition of Straight ngle m. ngles are congruent if and only if their measures are equal n. is a right angle if and only if m = 90 o. n angle is acute if and only if its measure, x, is 0 < x < 90 p. Segments are congruent if and only if their lengths are equal. q. bisects T if and only if T r. bisects if and only if it passes through the midpoint of s. M is the midpoint if and only if M = M and -M- t. n angle is obtuse if and only if its measure, x, is 90 < x < 80 u. m = 80 if and only if it s a straight angle

2 Int. Geometry Unit Quiz Review (Lessons -4) POSTULTS. Segment ddition Postulate. ngle ddition Postulate v. If is between and, then + = w. If T is in the interior of, then m T = m T = m irections 4-7: Name the definition, property, postulate, or theorem that justifies each statement. Refer to the diagram: 4. T = T 5. If S bisects P, then m S = m SP S P 6. If is the midpoint of T, then = T T 7. m S + m SP = m P irections 8: In the following two algebraic proofs, justify each statement with a property from algebra. Statement Reason x + = Given a. x = 8 a. b. x = 4 b. 9. omplete the following proof. Given: Prove:

3 Int. Geometry Unit Quiz Review (Lessons -4) 0. Write an indirect proof. Given: m m Prove: does not bisect. Write a proof. Given: = ; = Prove: =. Write an indirect proof. Given: y + 5 Prove: y. Given: G = FH Prove: F = GH F G H

4 Int. Geometry Unit Quiz Review (Lessons -4) 4 4. Given: m m Prove: m m Selected nswers:. c. j. f 4. e 5. g 6. l 7. a 8. h 9. i 0. k. b. d. q 4. s 5. r 6. m 7. p 8. n 9. o 0. t. u. v. w 4. Reflexive Property 5. ef. of an angle bisector 6. Midpoint efinition 7. ngle ddition Postulate 8. a. Subtraction b. ivision Note with the proofs, there are multiple solutions to these problems 9.. m = m. Reflexive Po iagram. m = m. Given. m + m = m + m. ddition Po and 4. m + m = m 4. ngle ddition iagram m + m = m Postulate 5. m = m 5. Substitution Po and 4

5 Int. Geometry Unit Quiz Review (Lessons -4) 5 0. Temporarily assume bisects y the definition of an angle bisector. This contradictions the given information m m, therefore our assumption must be false and does not bisect.. = ; =. Given. + = +. ddition Po. + =. Segment ddition iagram + = Postulate 4. = 4. Substitution Po and. Temporarily assume y =. Then y + = ( ) + = 5 This contradicts our given information, y + 5. Therefore our assumption must be false and y.. F+FG=G and. Segment ddition iagram FG+GH=FH Postulate. G = FH. Given. F+FG = FG+GH. Substitution Po and 4. FG = FG 4. Reflexive Po iagram 5. F = GH 5. Subtraction Po and 4 4. Temp. assume that m = m. The ngle ddition Postulate allows us to say m = m + m and m = m + m. Since we assumed m = m by the Substitution Po we get m + m = m + m. The m = m by the Reflexive Po which means by the Subtraction Po we have m = m, but this contradicts the given information that : m m which means our assumption is false and m m.