CSG AB BC; D is the midpoint of AC 1. Given. 2. AD CD 2. Definition of Midpoint 3. BD BD 3. Reflexive Property 4. ABD CBD 4.?
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1 LIFORNI STNRS TEST LIFORNI STNRS TEST Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition defining mathematical terms to correspond with physical objects inferring a general truth by eamining a number of specific eamples SG008 3 onsider the arguments below. I. Every multiple of 4 is even. 376 is a multiple of 4. Therefore, 376 is even. II. number can be written as a repeating decimal if it is rational. Pi cannot be written as a repeating decimal. Therefore, pi is not rational. Which one(s), if any, use deductive reasoning? I only II only both I and II Use the proof to answer the question below. Given: ; is the midpoint of Prove: In the diagram below, 4. neither I nor II SG00 Statement Reason. ; is the midpoint of. Given l m Theorem: triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in, and are both obtuse. Which theorem will Eduardo use to reach a contradiction? If two angles of a triangle are equal, the sides opposite the angles are equal... efinition of Midpoint Refleive Property 4. 4.? What reason can be used to prove that the triangles are congruent? S S SS t Which of the following conclusions does not have to be true? 3 and 4 are supplementary angles. Line l is parallel to line m. If two supplementary angles are equal, the angles each measure 90. The largest angle in a triangle is opposite the longest side. The sum of the measures of the angles of a triangle is 80. SG000 SSS SG SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
2 LIFORNI STNRS TEST LIFORNI STNRS TEST 6 In the figure below, >. 7 Use the proof to answer the question belowġiven: 3 Prove: 4 l 4 3 m t If we assume that m = m, it follows that =. This contradicts the given statement that >. What conclusion can be drawn from this contradiction? m = m m m m = m m m SG004 Statement Reason. 3. Given. ; 3 4.? Transitive Property What reason can be used to justify statement? omplements of congruent angles are congruent. Vertical angles are congruent. Supplements of congruent angles are congruent. orresponding angles are congruent. SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
3 LIFORNI STNRS TEST LIFORNI STNRS TEST 8 Two lines in a plane always intersect in eactly one point. Which of the following best describes a countereample to the assertion above? coplanar lines parallel lines perpendicular lines intersecting lines conditional statement is shown below. If a quadrilateral has perpendicular diagonals, then it is a rhombus. Which of the following is a countereample to the statement above? Students in a class rewrote theorems in their own words. One student wrote the following statement. The area of a parallelogram is the product of any base (b) and any height (h). Which figure shows a countereample to prove the statement false? 3 Which triangles must be similar? two obtuse triangles two scalene triangles with congruent bases two right triangles two isosceles triangles with congruent verte angles SG SG0030 Which figure can serve as a countereample to the conjecture below? h 4 Which of the following facts would be sufficient to prove that triangles and E are similar? If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram. rectangle rhombus b b h square trapezoid SG094 SG06 b E 0 Given: TRP is an isosceles trapezoid with diagonals RP and T. Which of the following must be true? RP T RP T RP T b h h E and E are congruent. E is a right angle. and E are parallel. and are congruent. SG0044 RP bisects T SG0060 SG00 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
4 LIFORNI STNRS TEST LIFORNI STNRS TEST Parallelogram is shown below. 7 In parallelogram FGHI, diagonals IG and FH are drawn and intersect at point M. Which of the following statements must be true? FGI must be an obtuse triangle. 9 Which of the following statements must be true if GHI JKL? H K In the figure below, F and. E HIG must be an acute triangle. FMG must be congruent to HMG. GMH must be congruent to IMF. SG009 G I Which pair of triangles can be established to be congruent to prove that? 8 Which of the following best describes the triangles shown below? J L F E 6 and E and E and E and E SG046 If and XYZ are two triangles such that =, which of the following would XY YZ be sufficient to prove the triangles are similar? The two triangles must be scalene. The two triangles must have eactly one acute angle. t least one of the sides of the two triangles must be parallel. The corresponding sides of the two triangles must be proportional. SG Which method listed below could not be used to prove that two triangles are congruent? Which additional information would be enough to prove that EF? E EF E SG007 X Y Z X Y SG08 both similar and congruent similar but not congruent congruent but not similar neither similar nor congruent SG00478 Prove all three sets of corresponding sides congruent. Prove all three sets of corresponding angles congruent. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle. Prove that two angles and an included side of one triangle are congruent to two angles and an included side of the other triangle. SG0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 3 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
5 LIFORNI STNRS TEST LIFORNI STNRS TEST Given: and intersect at point E; 3 Given: E is the midpoint of ; Which of the following sets of numbers could represent the lengths of the sides of a triangle?,, 3, 3, 7 What values of a and b make quadrilateral MNOP a parallelogram? N O 4, 4, 8 3 E 4 Which theorem or postulate can be used to prove E E? E Which of the following statements must be true? 6,, SG004 In the accompanying diagram, parallel lines l and m are cut by transversal t. t l 3a b M a=, b= a=, b= 4a + b P 3 SSS E E m 34 a=, b= 7 7 S SS SG0074 SG0078 Which statement about angles and must be true? 34 a=, b= 7 7 SG063 4 In the figure below, n is a whole number. What is the smallest possible value for n? n n. is the complement of. is the supplement of. and are right angles. SG Quadrilateral is a parallelogram. If adjacent angles are congruent, which statement must be true? Quadrilateral is a square. Quadrilateral is a rhombus. Quadrilateral is a rectangle. Quadrilateral is an isosceles trapezoid. SG SG009 4 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
6 LIFORNI STNRS TEST LIFORNI STNRS TEST 9 For the quadrilateral shown below, what is m a + m c? 9 o a o c o 3 o SG06 3 The diameter of a circle is meters. If point P is in the same plane as the circle, and is 6 meters from the center of the circle, which best describes the location of point P? Point P must be on the circle. Point P must be inside the circle. Point P may be either outside the circle or on the circle. Point P may be either inside the circle or on the circle. 3 Given: p q; m n; m = 7 SG right circular cone has radius inches and height 8 inches. 8 in. in. What is the lateral area of the cone? (Lateral area of cone = πrl, where l = slant height ) 40π sq in. l 34 Figure is a kite. 0 cm 0 cm 6 cm 8 cm 8 cm 7 cm cm 7 cm What is the area of figure, in square centimeters? 30 If is a parallelogram, what is the length of segment? q 44π sq in. π 39 sq in. π 89 sq in SG E What is m? m n p 3 SG07 If a cylindrical barrel measures inches in diameter, how many inches will it roll in 8 revolutions along a smooth surface? π in. 68π in π in. 8π in. SG SG004 SG036 6 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
7 LIFORNI STNRS TEST LIFORNI STNRS TEST 36 sewing club is making a quilt consisting of squares with each side of the square measuring 30 centimeters. If the quilt has five rows and five columns, what is the perimeter of the quilt? 0 cm 38 The four sides of this figure will be folded up and taped to make an open bo. centimeters 39 classroom globe has a diameter of 8 inches. 4 The rectangle shown below has length 0 meters and width 0 meters. 4 m 4 m 4 m 4 m 300 cm 600 cm 900 cm SG0 4 m 4 m 4 m 4 m 37 The minute hand of a clock is inches long. What is the area of the circle, in square inches, created as the hand sweeps an hour? 0π 0π π 00π SG03 What will be the volume of the bo? 0 cm 3 7 cm 3 00 cm 3 cm 3 SG Which of the following is the approimate surface area, in square inches, of the globe? (Surface rea = 4πr ) SG038 Vik is constructing a spherical model of Earth for his science fair project. His model has a radius of 4 inches. Since roughly 7% of Earth s surface is covered by water, he wanted to paint 7% of his model blue to illustrate this fact. pproimately how many square inches on his model will be painted blue? ( Surface rea = 4πr ) 4 If four triangles are removed from the rectangle as shown, what will be the area of the remaining figure? 36 m 44 m 68 m 84 m SG000 If RSTW is a rhombus, what is the area of WXT? S R X 60 o T W ,407 7,877 SG SG007 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
8 LIFORNI STNRS TEST LIFORNI STNRS TEST What is the area, in square units, of the trapezoid shown below? y (0, ) (8, ) 0 (, 0) The figure below is a square with four congruent parallelograms inside. SG06 4 What is the area, in square meters (m), of the trapezoid shown below? m m m m SG What is the area, in square inches (in.), of the triangle below? 47 What is the area, in square centimeters, of rhombus RSTV if RT = 6 cm and SV = cm? R S V T SG Lea made two candles in the shape of right rectangular prisms. The first candle is cm high, 8 cm long, and 8 cm wide. The second candle is cm higher but has the same length and width. How much additional wa was needed to make the taller candle? 30 cm cm cm 3 80 cm 3 SG06 0 Two angles of a triangle have measures of and 6. Which of the following could not be a measure of an eterior angle of the triangle? in. 0 in. 0 in. 48 The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the areas of the two squares? to 3 4 to 9 30 SG007 The sum of the interior angles of a polygon is the same as the sum of its eterior angles. What type of polygon is it? What is the area, in square units, of the shaded portion? SG to 7 6 to 8 SG0003 quadrilateral heagon octagon decagon SG SG0 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
9 LIFORNI STNRS TEST LIFORNI STNRS TEST What is m? 4 In the figure below,. 6 regular polygon has sides. What is the measure of each eterior angle? 8 What is m WZX? ( + 40)º ( 40)º 30 3º V SG00039 W SG0086 What is the value of? What is m? 36 o 88 o Y º Z X 3 If the measure of an eterior angle of a regular polygon is 0, how many sides does the polygon have? SG004 SG0044 The measures of the interior angles of a pentagon are, 6,4 6, 6, and 6 +. What is the measure, in degrees, of the largest angle? SG300 9 What is the measure of an eterior angle of a regular heagon? SG008 SG SG0070 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 3 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
10 LIFORNI STNRS TEST LIFORNI STNRS TEST Geometr y 60 diagram from a proof of the Pythagorean theorem is pictured below. a c Which statement would not be used in the proof of the Pythagorean theorem? The area of a triangle equals ab. The four right triangles are congruent. The area of the inner square is equal to half of the area of the larger square. The area of the larger square is equal to the sum of the areas of the smaller square and the four congruent triangles. b SG09 6 right triangle s hypotenuse has length. If one leg has length, what is the length of the other leg? SG new pipeline is being constructed to re-route its oil flow around the eterior of a national wildlife preserve. The plan showing the old pipeline and the new route is shown below. 60 miles NEW PIPELINE OL PIPELINE 3 miles bout how many etra miles will the oil flow once the new route is established? 63 What is the height of this rectangle? 64 unit 6 units units 3 units 8 7? SG00473 Marsha is using a straightedge and compass to do the construction shown below. P 6 Given: angle What is the first step in constructing the angle bisector of angle? raw ray. raw a line segment connecting points and. From points and, draw equal arcs that intersect at. From point, draw an arc that intersects the sides of the angle at points and. SG l SG006 Which best describes the construction Marsha is doing? a line through P parallel to line l a line through P intersecting line l a line through P congruent to line l a line through P perpendicular to line l SG006 4 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
11 LIFORNI STNRS TEST LIFORNI STNRS TEST 66 Scott is constructing a line perpendicular to line l from point P. Which of the following should be his first step? P l 67 Which triangle can be constructed using the following steps?. Put the tip of the compass on point.. Open the compass so that the pencil tip is on point. 3. raw an arc above. 68 What geometric construction is shown in the diagram below? 69 The diagram shows. y P 4. Without changing the opening, put the metal tip on point and draw an arc intersecting the first arc at point.. raw and. l P P l l right obtuse scalene equilateral SG03 an angle bisector a line parallel to a given line an angle congruent to a given angle a perpendicular bisector of a segment SG009 Which statement would prove that is a right triangle? ( slope )( slope ) = ( slope )( slope ) = distance from to = distance from to distance from to = (distance from to ) SG0047 SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
12 LIFORNI STNRS TEST LIFORNI STNRS TEST 70 Figure O is a parallelogram. y (a, b) (a + c, b) O (c, 0) What are the coordinates of the point of intersection of the diagonals? 7 What type of triangle is formed by the points (4, ), (6, ), and (, 3 )? right equilateral isosceles scalene 7 The point ( 3, ) lies on a circle whose SG03 equation is ( + 3 ) + ( y + ) = r. Which of the following must be the radius of the circle? What is the length of line segment PQ shown below? y Q 6 (8, 7) 4 3 P (0, ) units 74 In the figure below, if sin =, what are cos and tan? 3 cos = and tan = 3 cos = and tan = 3 cos = 3 and tan = cos = 3 3 and tan = a b, c b, a+ c b, SG units 3 units 4 units SG In the figure below, sin = 07.. SG00493 a+ c a+ b, SG00 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 9 What is the length of? This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. SG0043
13 LIFORNI STNRS TEST LIFORNI STNRS TEST 76 pproimately how many feet tall is the streetlight? 77 Right triangle is pictured below foot ladder is leaning against a brick wall. The top of the ladder touches the wall feet (ft) above the ground. The bottom of the ladder is ft from the bottom of the wall. What is the sine of the angle formed by the ground and the base of the ladder? 79 In the accompanying diagram, m =3 and = 0. Which equation could be used to find in? h 3º 8. Which equation gives the correct value for? ft sin cos tan º sin 3 = 8. cos 3 = tan 8 = sin 8 = 0.6 SG ft ladder ft wall ft 3 =0 sin 3 =0 cos 3 =0 tan 3 0 = cos3 0 SG00 SG SG04 30 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 3 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
14 LIFORNI STNRS TEST LIFORNI STNRS TEST 80 The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 3 angle with the wall. Which is closest to the distance up the wall the ladder reaches? 8 Triangle JKL is shown below. K 8 What is the approimate height, in feet, of the tree in the figure below? 83 What is the approimate value of in the triangle below? 4 o L 00 ft 8 ft 3? J º 3. ft 4.8 ft 6.4 ft sin cos tan 3.33 Which equation should be used to find the length of JK? JK sin 4 = 8 8 sin 4 = JK JK cos 4 = 8 8 cos 4 = JK SG sin cos tan units 4. units 4.9 units 7.3 units sin cos tan SG ft SG06 SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 33 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
15 LIFORNI STNRS TEST LIFORNI STNRS TEST 84 If a = 3 3 in the right triangle below, what is the value of b? 8 What is the value of in the triangle below? 86 What is the value of, in inches? 88 In the circle below, and are chords intersecting at E. a 0 b c 7 in. E SG SG o SG0099 If E =, E =, and E = 6, what is the length of E? square is circumscribed about a circle. What is the ratio of the area of the circle to the area of the square? 0 3 SG000 4 π π 4 SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 3 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
16 LIFORNI STNRS TEST LIFORNI STNRS TEST 89 R is tangent to a circle, whose center is, at point. is a diameter. R 90 In the figure below, is tangent to circle O at point, secant intersects circle O at points and, m = 70, and m = o 9 In the circle shown below, the measure of PR = 40 and the measure of RPQ = 0. 40º 0º P 9 QS is a diameter of the circle below, and QS PR. P Q R º O R O 0 o Q What is m R? SG086 What is m? What is the measure of PQ? SG0003 S If mp QR = 06, what is mps? SG07 SG The vertices of are (, ), (3, 4), and (, 3). If is translated unit down and 3 units to the left to create EF, what are the coordinates of the vertices of EF? (0, ), E(, ), F(, 3) (0, ), E(0, 3), F(, ) (, ), E(0, 3), F(, 0) (, 0), E(0, 3), F(, ) SG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 37 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
17 LIFORNI STNRS TEST LIFORNI STNRS TEST 94 If triangle is rotated 80 degrees about the origin, what are the coordinates of? y (, 4) (, 4) ( 4, ) ( 4, ) SG Trapezoid below is to be translated to trapezoid by the following motion rule. (, y) ( + 3, y 4) y What will be the coordinates of verte? (, 3) (, ) ( 6, ) ( 8, 3) 96 Which epression describes the translation of a point from ( 3 4 to 4, )?, ) ( 7 units left and units up 7 units right and units up 7 units left and units down 7 units right and units down SG007 SG04 38 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 39 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
18 LIFORNI ST N RS TE ST LIFORNI STNRS TEST Question Number orrect nswer Standard Year of Release GE.0 GE.0 GE.0 GE.0 GE.0 GE.0 GE.0 GE3.0 GE3.0 GE3.0 GE3.0 GE3.0 GE4.0 GE4.0 GE4.0 GE4.0 GE4.0 GE4.0 GE4.0 GE4.0 GE.0 GE.0 GE.0 GE6.0 GE6.0 GE7.0 GE7.0 GE7.0 GE7.0 GE7.0 GE7.0 GE7.0 GE8.0 GE8.0 GE Question Number orrect nswer Standard Year of Release 36 GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education. 4 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
19 LIFORNI ST N RS TE ST Question Number orrect nswer Standard Year of Release 7 GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE GE This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.
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