Name____________________________ Date________________ Period__________ SECONDARY MATH I – BENCHMARK 3 (Units 6, 7, 8) PART I – MULTIPLE CHOICE DIRECTIONS: PLEASE CIRCLE THE CORRECT RESPONSE 1) Which of the following is the precise definition for a circle? a. The set of all points equidistant from a point called the center. b. A shape formed by two rays with a common endpoint called the vertex c. Two endpoints of a line segment and all the points between them. d. Lines that intersect to form a right angle. 2) Describe the transformation that takes point (, ) to point ( − 3, + 5). a. Translate right 3 and up 5 b. Translate right 3 and down 5 c. Translate left 3 and up 5 d. Translate left 3 and down 5 3) How many lines of symmetry does a square have? a. 2 b. 4 c. 6 d. Infinitely many 4) Which of the following counter-clockwise rotations about the center of the figure will carry the rectangle displayed below onto itself? a. 90 degrees b. 180 degrees c. 270 degrees d. 300 degrees 5) Which transformation would carry figure 1 onto figure 2? a. Rotation b. Reflection c. Dilation d. Translation 6) What transformation is not a rigid motion a. Rotation b. Reflection c. Dilation d. Translation 7) Which two rigid motion transformations could be used to prove quadrilateral ABCD is congruent to quadrilateral KLMN? a. b. c. d. Reflection over the y-axis, translation Rotation about the origin, translation Translation, reflection over the x-axis Reflection, over the x-axis, reflection over the y-axis 8) Which of the following show the figure (to the right) reflected over the x-axis? a. c. b. d. ̅̅̅̅ 9) Which side of trapezoid JKHI corresponds to a. ̅̅̅̅ b. ̅̅̅ ̅̅̅ c. ̅ ̅ d. 10) Which method of proving triangle congruency is missing from the following list: ASA, SSS, SAA? a. AAA b. SAS c. SSA d. No method is missing 11) Which triangle congruence can be used to prove that the two triangles are congruent? a. AAS b. SSS c. SAS d. SSA 12) What additional information is required in order to know that the triangles are congruent by ASA? ̅̅̅̅ a. ̅̅̅̅ ≅ ̅̅̅̅ ≅ ̅̅̅̅ b. ̅̅̅̅ c. ̅̅̅̅ ≅ ̅̅̅̅ ≅ ̅̅̅̅ d. 13) Given ∆NOP, what construction was performed? a. Copy a segment b. Copy an angle c. Perpendicular bisector d. Angle bisector 14) Given vertices at (−5, −1), (3,3), and (6, −3), what would be the fourth vertex be in order for the shape to be a rectangle? a. (−2, −6) b. (−2,6) c. (−3,7) d. (−2, −7) 15) A line contains the points (−3,5) and is parallel to the line = −2 + 7. What is the equation of the line? a. = −2 + 8 b. = −2 − 1 c. = −2 + 1 d. = −2 + 11 16) Given the line: 1 = − − 7, what is the slope of a line parallel to it and the 2 slope of a line perpendicular to it? 1 a. Parallel =− 2 b. Parallel =2 1 c. Parallel =− d. Parallel = −2 2 17) What is the perimeter of the triangle to nearest whole number? a. 12 units b. 18 units c. 40 units d. 50 units perpendicular = −2 perpendicular = perpendicular =2 perpendicular = 1 2 1 2 18) Given a function, (), describe what happens to the graph of the function when it is replaced by ( + 2). a. Translate left 2 units b. Translate right 2 units c. Translate up 2 units d. Translate down 2 units 19) ( ) = 6 intercept? a. b. c. d. − 3 under goes a vertical translation of −4, what is the new y- 2 −1 −7 21 20) Given the function, () = −(3 ) + , (displayed on the right) find the value of . a. −3 b. 1 c. 3 d. 4 Name____________________________ Date________________ Period__________ SECONDARY MATH I – BENCHMARK 3 (Units 6, 7, 8) PART II – CONSTRUCTED RESPONSE DIRECTIONS: WRITE YOUR ANSWERS IN THE SPACES PROVIDED 1) Construct the bisector of the angle below. (3pts) 2) Given quadrilateral PQRS: a. Create P’Q’R’S’ by transforming quadrilateral PQRS according to the rule ( + 3, + 5). List the coordinates of the new vertices of P’Q’R’S’. (4pts) b. Describe the transformation. (2pts) c. Prove that PQRS is a Parallelogram. (2pts) d. Is Parallelogram P’Q’R’S’ a rectangle, square and/or rhombus? Justify your answer. (2pts) 3) Refer to the figure on the right for the following questions: a. What transformation maps ∆ onto ∆? (1pt) b. Is ∠ ≅ ∠? How do you know? (2pts) ̅̅̅̅ ≅ ̅̅̅̅ c. Is ? How do you know? (2pts) d. Is ̅̅̅̅ ≅ ̅̅̅̅ ? How do you know? (2pts) e. Is ∆ ≅ ∆? What triangle congruency criterion proves it? (2pts) PART I - MULTIPLE CHOICE ANSWERS QUESTION ANSWER STANDARD QUESTION ANSWER STANDARD 1 A G.CO.1 11 C G.CO.8 2 C G.CO.2 12 A G.CO.8 3 B G.CO.3 13 C G.CO.12 4 B G.CO.3 14 D G.GPE.4 5 D G.CO.5 15 B G.GPE.5 6 C G.CO.6 16 C G.GPE.5 7 A G.CO.6 17 C G.GPE.7 8 A G.CO.5 18 A F.BF.3 9 A G.CO.7 19 C F.BF.3 10 B G.CO.8 20 D F.BF.3 PART II – CONSTRUCTED RESPONSE ANSWERS QUESTION 1 ANSWER STANDARD POINTS G.CO.12 Construct the angle bisector 3 points QUESTION 2 ANSWER STANDARD POINTS a. G.CO.5 Transform figures 4 points ’ (1,7), ’ (4,3), ’ (1, −1), ’ (−2,3) b. G.CO.2 right three and up five Describe Transformation 2 points c. BE CONSIDERATE OF OTHER POSSIBLE PROOFS. 4 = = − 3 4 = = 3 Because PQRS is a quadrilateral with opposite sides parallel, it is a G.CO.1 Precise definitions G.GPE.4 2 points Use coordinates to prove simple geometric theorems algebraically parallelogram. d. G.CO.1 = = = = 5 Precise definitions Since all four sides are the same length and opposite sides are parallel it is a G.GPE.4 RHOMBUS. It is not a square since the Use coordinates to prove slope of the adjacent lines are not simple geometric opposite reciprocals. theorems algebraically 2 points QUESTION 3 ANSWER a. (−, −) A 180 degree rotation with the origin as the center of rotation b. yes, because a rotation is a rigid motion transformation that preserves angle measurement c. yes, because a rotation is a rigid motion transformation that preserves length d. yes, because a rotation is a rigid motion transformation that preserves length e. yes, by SAS congruency STANDARD POINTS G.CO.2 Represent transformations in the 1 point coordinate plane G.CO.6 Definition of congruence in terms 2 points of rigid motion G.CO.6 Definition of congruence in terms 2 points of rigid motion G.CO.6 Definition of congruence in terms 2 points of rigid motion G.CO.7 Show that two triangles are congruent 2 points

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# SECONDARY MATH I – BENCHMARK 3 (Units 6, 7, 8)