CA LI FOR N I A STA N DA R DS TE ST CSG00185 C D CSG10066
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1 LI FOR N I ST N R S TE ST 1 Wic of te following est descries deductive reasoning? using logic to draw conclusions ased on accepted statements accepting te meaning of a term witout definition defining matematical terms to correspond wit pysical ojects inferring a general trut y examining a numer of specific examples SG onsider te arguments elow. I. Every multiple of 4 is even. 376 is a multiple of 4. Terefore, 376 is even. II. numer can e written as a repeating decimal if it is rational. Pi cannot e written as a repeating decimal. Terefore, pi is not rational. Wic one(s), if any, use deductive reasoning? I only II only ot I and II 2 In te diagram elow, 1 4. neiter I nor II SG00552 l m Teorem: triangle as at most one otuse angle. Eduardo is proving te teorem aove y contradiction. He egan y assuming tat in, and are ot otuse. Wic teorem will Eduardo use to reac a contradiction? t Wic of te following conclusions does not ave to e true? 3 and 4 are supplementary angles. Line l is parallel to line m If two angles of a triangle are equal, te sides opposite te angles are equal. If two supplementary angles are equal, te angles eac measure 90. Te largest angle in a triangle is opposite te longest side. Te sum of te measures of te angles of a triangle is 180. SG00025 SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
2 LI FOR N I ST N R S TE ST 5 Use te proof to answer te question elow. Given: ; is te midpoint of Prove: Statement Reason 1. ; is te midpoint of 1. Given efinition of Midpoint Reflexive Property 4. 4.? Wat reason can e used to prove tat te triangles are congruent? S S SS SSS SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
3 LI FOR N I ST N R S TE ST 6 In te figure elow, >. If we assume tat m = m, it follows tat =. Tis contradicts te given statement tat >. Wat conclusion can e drawn from tis contradiction? m = m m m m = m m m SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
4 LI FOR N I ST N R S TE ST 7 Use te proof to answer te question elowġiven: 2 3 Prove: l 4 3 m t Statement Reason Given ; ? Transitive Property Wat reason can e used to justify statement 2? omplements of congruent angles are congruent. Vertical angles are congruent. Supplements of congruent angles are congruent. orresponding angles are congruent. SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
5 LI FOR N I ST N R S TE ST 8 Two lines in a plane always intersect in exactly one point. Wic of te following est descries a counterexample to te assertion aove? coplanar lines parallel lines perpendicular lines intersecting lines 11 conditional statement is sown elow. If a quadrilateral as perpendicular diagonals, ten it is a romus. Wic of te following is a counterexample to te statement aove? SG Wic figure can serve as a counterexample to te conjecture elow? If one pair of opposite sides of a quadrilateral is parallel, ten te quadrilateral is a parallelogram. rectangle romus square trapezoid SG Given: TRP is an isosceles trapezoid wit diagonals RP and T. Wic of te following must e true? SG20216 RP T RP T RP T RP isects T SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
6 LI FOR N I ST N R S TE ST 12 Students in a class rewrote teorems in teir own words. One student wrote te following statement. Te area of a parallelogram is te product of any ase () and any eigt (). Wic figure sows a counterexample to prove te statement false? 13 Wic triangles must e similar? two otuse triangles two scalene triangles wit congruent ases two rigt triangles two isosceles triangles wit congruent vertex angles SG Wic of te following facts would e sufficient to prove tat triangles and E are similar? E E and E are congruent. E is a rigt angle. and E are parallel. and are congruent. SG00544 SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
7 LI FOR N I ST N R S TE ST 15 Parallelogram is sown elow. E 17 In parallelogram FGHI, diagonals IG and FH are drawn and intersect at point M. Wic of te following statements must e true? FGI must e an otuse triangle. HIG must e an acute triangle. FMG must e congruent to HMG. GMH must e congruent to IMF. SG00559 Wic pair of triangles can e estalised to e congruent to prove tat? 18 Wic of te following est descries te triangles sown elow? and E and E and 30 E and E SG If and XYZ are two triangles suc tat =, wic of te following would XY YZ e sufficient to prove te triangles are similar? 60 X Y Z X Y ot similar and congruent similar ut not congruent congruent ut not similar neiter similar nor congruent SG10218 SG Tis is a sample of alifornia Standards Test questions. Tis is NOT an operational test form. Test scores cannot e projected ased on performance on released test questions. opyrigt 2009 alifornia epartment of Education.
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