Virginia Mathematics Checkpoint Assessment GEOMETRY G.5. Topic: Triangles

Transcription

1 Virginia Mathematics Checkpoint Assessment GEOMETRY G.5 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.5 Page 1

2 Checkpoint Items 1. Directions: After showing your thinking, write your answers in the series of boxes below. You must complete each box. m A = (10x), m B = (x 2 ), and m C = (21x). In ABC, order the sides from longest to shortest. Write the sides in order in the boxes provided below.,, Geometry Checkpoint G.5 Page 2

3 2. Directions: After showing your thinking, write your answers in the series of boxes below. You must complete each box. Right triangle MPQ has acute angles M and Q. m M = (3x + 9) and m Q = (4x + 4). Order the sides of the triangle from longest to shortest. Write the sides in order in the boxes provided below. MQ PQ MP M P Q,, Geometry Checkpoint G.5 Page 3

4 3. Directions: After showing your thinking, write your answers in the series of boxes below. You must complete each box. In triangle PQR, m P = 60, m Q = 77 and m R = 43. Order the sides of the triangle from longest to shortest. Write the sides in order in the boxes provided below. A list of the sides is shown below. QP QR PR,, Geometry Checkpoint G.5 Page 4

5 4. Directions: After showing your thinking, write your answers in the series of boxes below. You must complete each box. Triangle EFG has side lengths EG = 5, EF = 10 and FG = 3 2. Write the angle numbers in order from greatest to least. E 1 F 2 3 G,, Geometry Checkpoint G.5 Page 5

6 5. Directions: After showing your thinking, write your answers in the series of boxes below. You must complete each box. In triangle UWV, WV = 12, VU = 10 and UW = 11. List the angles in order from least to greatest based on the measurements given. A list of angles is shown below. U V W,, Geometry Checkpoint G.5 Page 6

7 6. Directions: After showing your thinking, write your answers in the boxes provided. You must complete each box. The sum of three side lengths is 174. The three lengths are represented by the following expressions (4x 8), (5x + 3) and (6x 1). Find the value of x and then determine whether the lengths could form a triangle. x = Can this form a triangle? (write yes or no) Geometry Checkpoint G.5 Page 7

8 7. Directions: Circle the box you want to select. You must select all correct answers. A side length of 23 could be combined with what two other sides to form a triangle? 10 and and and and 40 7 and and 89 Geometry Checkpoint G.5 Page 8

9 8. Directions: After showing your thinking, write your answers in the boxes below. Your answers should be fractions. Use improper fractions, if necessary. Do not use mixed numbers. If two side lengths are 3 and 5, what are possible lengths of the third side, x? 4 8 < x < Geometry Checkpoint G.5 Page 9

10 9. Directions: After showing your thinking, write your answers in the boxes below to complete the inequality. Your answers should be decimals to the tenths place. Two lengths of a triangle are 1.8 and 2.9. What are the possible lengths of the third side? < x < Geometry Checkpoint G.5 Page 10

11 10. Directions: After showing your thinking, circle the box you want to select. You must select all correct answers. The Bermuda Triangle connects Miami to Bermuda to Puerto Rico. If the distance from Miami to Bermuda is approximately 1,040 miles and the distance from Bermuda to Puerto Rico is approximately 970 miles, then what are possible distances from Puerto Rico to Miami (since the distance must form a triangle)? 50 miles 100 miles 200 miles 500 miles 1,000 miles 2,000 miles 2,500 miles 3,000 miles Geometry Checkpoint G.5 Page 11

12 11. Directions: After showing your thinking, circle the box you want to select. A tree and its shadow create a right triangle. The angle of elevation from the ground to the tree is 47. Which one is longer, the height of the tree or the length of the shadow? 47 Shadow Length Tree Height Geometry Checkpoint G.5 Page 12

13 Checkpoint Solutions SOL G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will a) order the sides by length, given the angle measures; b) order the angles by degree measure, given the side lengths; c) determine whether a triangle exists; and d) determine the range in which the length of the third side must lie. These concepts will be considered in the context of real-world situations. Essential Knowledge and Skills a. Order the sides of a triangle by their lengths when given the measures of the angles b. Order the angles of a triangle by their measures when given the lengths of the sides c. Given the lengths of three segments, determine whether a triangle could be formed d. Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie e. Solve real-world problems given information about the lengths of sides and/or measures of angles in triangles Item Answer/Solution SOL/EKS Code 1 AB, BC, AC G.5aa 2 MQ, MP, PQ 3 PR, QR, QP G.5aa G.5aa 4 2, 1, 3 G.5bb 5 W, V, U G.5bb 6 12, yes G.5cc 7 G.5cc 8 G.5dd < x < 4.7 G.5dd 10 G.5ad 11 Tree Height G.5de Essential Knowledge and Skills Order the sides of a triangle by their lengths when given the measures of the angles Order the sides of a triangle by their lengths when given the measures of the angles Order the sides of a triangle by their lengths when given the measures of the angles Order the angles of a triangle by their measures when given the lengths of the sides Order the angles of a triangle by their measures when given the lengths of the sides Given the lengths of three segments, determine whether a triangle could be formed Given the lengths of three segments, determine whether a triangle could be formed Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie Solve real-world problems given information about the lengths of sides and/or measures of angles in triangles Geometry Checkpoint G.5 Page 13