Virginia Mathematics Checkpoint Assessment GEOMETRY G.7. Topic: Triangles

Transcription

1 Virginia Mathematics Checkpoint Assessment GEOMETRY G.7 Topic: Triangles Standards of Learning Blueprint Summary Reporting Category Geometry SOL Number of Items Reasoning, Lines, and G.1(a-d), G.2(a-c), G.3(a-d), 18 Transformations G.4(a-g) Triangles G.5(a-d), G.6, G.7, G.8 14 Polygons, Circles, and Three- G.9, G.10, G.11(a-c), G.12, 18 Dimensional Figures G.13, G.14(a-d) Excluded from Testing None Number of Operational Items 50 Number of Field-Test Items 10 Total Number of Items on Test 60 Virginia Mathematics SOL Test Cut Scores Failing Scores Passing Scores Test Basic Proficient Advanced Minimum Minimum Minimum Minimum # correct % correct # correct % correct # correct % correct Math 3 16 of 40 40% 26 of 40 65% 36 of 40 90% Math 4 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 5 18 of 50 36% 31 of 50 62% 45 of 50 90% Math 6 16 of 50 32% 28 of 50 56% 45 of 50 90% Math 7 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 8 17 of 50 34% 31 of 50 62% 46 of 50 92% Algebra I n/a n/a 25 of 50 50% 45 of 50 90% Geometry n/a n/a 25 of 50 50% 44 of 50 88% Algebra II n/a n/a 27 of 50 54% 43 of 50 86% Geometry Checkpoint G.7 Page 1

2 Checkpoint Items 1. Directions: After showing your thinking, circle the box you want to select. You must select all correct answers. Which sets of side lengths represent triangles where ABC~ DEF by Side- Side-Side similarity? Geometry Checkpoint G.7 Page 2

3 2. Directions: Circle the pair of triangles you want to select. Which pair of triangles could be proven similar by Side-Side-Side similarity? Geometry Checkpoint G.7 Page 3

4 3. Directions: After showing your thinking, circle the box you want to select. If ABC DEF and CB FE, which method would be used to prove that ACB~ DFE? A C B D F E Side-Angle-Side Similarity Side-Side-Side Similarity Angle-Angle Similarity Geometry Checkpoint G.7 Page 4

5 4. Directions: After showing your thinking, circle the pairs of triangles you want to select. You must select all correct answers. Figures not drawn to scale. If x = 17, which pairs of triangles are similar? Geometry Checkpoint G.7 Page 5

6 5. Directions: After showing your thinking, write your answer in the box as a fraction. Your answer should be an improper fraction, if necessary. Do not use mixed numbers. In order for the triangles in the diagram to be similar by Side-Angle-Side, the sides must be in proportion. Use proportions to solve for the value of x. x = Geometry Checkpoint G.7 Page 6

7 6. Directions: After showing your thinking, write your answer in the boxes provided. In order for ACB~ CDE, what are the values for x and y? x = y = Geometry Checkpoint G.7 Page 7

8 7. Directions: After showing your thinking, write your answers in the boxes provided. Find the value of x and then find the length of KL in order for DKC~ LKM. D C 18 K (4x 9) M L x = KL = Geometry Checkpoint G.7 Page 8

9 8. Directions: After showing your thinking, graph the point on the grid provided and then write the coordinates in the boxes below. Find the coordinates for M, so that KRB~ MQC if K( 1, 1), R(1, 1), B(1, 2), Q(2, 4), and C(2, 5). M = (, ) Geometry Checkpoint G.7 Page 9

10 9. Directions: After showing your thinking, graph the point on the grid provided and then write the coordinates in the boxes below. Find the coordinates for E, so that ABC~ DBE if A(0, 2), B(0, 0), C( 4, 0), and D(0, 5). E = (, ) Geometry Checkpoint G.7 Page 10

11 10. Directions: After showing your thinking, write your answers in the boxes provided. You must complete each box. A( 1, 3), B(3, 0) and C( 2, 2). In order for ABC~ DEF, complete the measurements for DEF so that the scale factor is 1:2. DE = EF = FD = Geometry Checkpoint G.7 Page 11

12 Checkpoint Solutions SOL G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs. Essential Knowledge and Skills a. Use definitions, postulates, and theorems to prove triangles similar b. Use algebraic methods to prove that triangles are similar c. Use coordinate methods, such as the distance formula, to prove two triangles are similar Item Answer/Solution SOL/EKS Code 1 G.7a Essential Knowledge and Skills Use definitions, postulates, and theorems to prove triangles similar Use definitions, postulates, and theorems to prove triangles similar 2 G.7a 3 Angle-Angle Similarity G.7a Use definitions, postulates, and theorems to prove triangles similar Use algebraic methods to prove that triangles are similar 4 G.7b 43 Use algebraic methods to prove that triangles are similar 5 G.7b 4 6 x = 11, y = 23 G.7b Use algebraic methods to prove that triangles are similar 7 x = 18, KL = 63 G.7b Use algebraic methods to prove that triangles are similar 8 (-4, -4) G.7c Use coordinate methods, such as the distance formula, to prove two triangles are similar 9 (-10, 0) G.7c Use coordinate methods, such as the distance formula, to prove two triangles are similar 10 DE = 10, EF = 2 29, Use coordinate methods, such as the distance formula, to G.7c prove two triangles are similar FD = 2 2 Geometry Checkpoint G.7 Page 12