Geometry Blizzard Bag Day 1

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1 Name: Class: Date: Geometry Blizzard Bag Day 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Draw and label a pair of opposite rays FG and FH. a. c. b. d. 2. K is the midpoint of JL. JK = 6x and KL = 3x + 3. Find J K, KL, and J L. a. J K = 1, KL = 1, J L = 2 c. J K = 12, KL = 12, J L = 6 b. J K = 6, KL = 6, J L = 12 d. J K = 18, KL = 18, J L = The tip of a pendulum at rest sits at point B. During an experiment, a physics student sets the pendulum in motion. The tip of the pendulum swings back and forth along part of a circular path from point A to point C. During each swing the tip passes through point B. Name all the angles in the diagram. a. AOB, BOC c. AOB, BOA, COB, BOC b. AOB, COB, AOC d. OAB, OBC, OCB 1

2 Name: 4. Tell whether FAC and 3 are only adjacent, adjacent and form a linear pair, or not adjacent. a. adjacent and form a linear pair b. only adjacent c. not adjacent 5. An angle measures 2 degrees more than 3 times its complement. Find the measure of its complement. a. 68 c. 23 b. 272 d Name all pairs of vertical angles. a. MLN and JLM ; JLK and KLN b. JLK and MLN; JLM and KLN c. JKL and MNL; JML and KNL d. JLK and JLM ; KLN and MLN 2

3 Name: 7. Find the coordinates for the image of EFG after the translation (x, y) (x 6, y + 2). Draw the image. a. c. b. d. 3

4 Name: 8. An animated film artist creates a simple scene by translating a kite against a still background. Write a rule for the translation of kite 1 to kite 2. a. (x, y) (x 6, y + 6) c. (x, y) (x 2, y + 2) b. (x, y) (x + 6, y 6) d. (x, y) (x + 2, y 2) 9. Name three collinear points. a. P, G, and N c. R, P, and G b. R, P, and N d. R, G, and N 10. Find the next item in the pattern 2, 3, 5, 7, 11,... a. 13 c. 15 b. 12 d. 17 4

5 Name: 11. The table shows the population 65 years and over by age and sex according to the US Census Bureau, Census 2000 Summary file. Make a conjecture based on the data. Population 65 Years and Over by Age and Sex: 2000 (numbers in thousands) 65 to 74 years 75 to 84 years 85 years and over Women 10,088 7,482 3,013 Men 8,303 4,879 1,227 a. Women outnumbered men in the 65 years and over population. b. Men outnumbered women in the 65 years and over population. c. There are more 65 years old and over in 2000 than in previous years. d. There are fewer 65 years old and over in 2000 than in previous years. 12. A gardener has 26 feet of fencing for a garden. To find the width of the rectangular garden, the gardener uses the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width of the rectangle. The gardener wants to fence a garden that is 8 feet long. How wide is the garden? Solve the equation for w, and justify each step. P = 2l + 2w Given equation 26 = 2(8) + 2w [1] 26 = w Simplify. 16 = = 2w Subtraction Property of Equality Simplify = 2w 2 [2] 5 = w Simplify. w = 5 Symmetric Property of Equality a. [1] Substitution Property of Equality [2] Division Property of Equality b. [1] Simplify [2] Division Property of Equality c. [1] Substitution Property of Equality [2] Subtraction Property of Equality d. [1] Subtraction Property of Equality [2] Simplify 13. Identify the property that justifies the statement. AB CD and CD EF. So AB EF. a. Reflexive Property of Congruence c. Symmetric Property of Congruence b. Substitution Property of Equality d. Transitive Property of Congruence 5

6 Name: 14. Use the given plan to write a two-column proof. Given: m 1 + m 2 = 90, m 3 + m 4 = 90, m 2 = m 3 Prove: m 1 = m 4 Plan: Since both pairs of angle measures add to 90, use substitution to show that the sums of both pairs are equal. Since m 2 = m 3, use substitution again to show that sums of the other pairs are equal. Use the Subtraction Property of Equality to conclude that m 1 = m 4. Complete the proof. Proof: Statements Reasons 1. m 1 + m 2 = Given 2. [1] 2. Given 3. m 1 + m 2 = m 3 + m 4 3. Substitution Property 4. m 2 = m 3 4. Given 5. m 1 + m 2 = m 2 + m 4 5. [2] 6. m 1 = m 4 6. [3] a. [1] m 3 + m 4 = 90 [2] Substitution Property [3] Subtraction Property of Equality b. [1] m 5 + m 6 = 90 [2] Substitution Property [3] Subtraction Property of Equality c. [1] m 3 + m 4 = 90 [2] Subtraction Property of Equality [3] Substitution Property d. [1] m 5 + m 6 = 90 [2] Addition Property of Equality [3] Substitution Property 6

7 Name: 15. Use the given flowchart proof to write a two-column proof of the statement AF FD. Flowchart proof: AB = CD; BF = FC Given AB + BF = AF FC + CD = FD Segment Addition Postulate AB + BF = FC + CD AF = FD AF FD Addition Property of Equality Complete the proof. Substitution Definition of congruent segments Two-column proof: Statements Reasons 1. AB = CD; BF = FC 1. Given 2. [1] 2. Addition Property of Equality 3. [2] 3. Segment Addition Postulate 4. AF = FD 4. Substitution 5. AF FD 5. Definition of congruent segments a. [1] AB + BF = AF ; FC + CD = FD [2] AF = FD b. [1] AF = FD [2] AB + BF = FC + CD c. [1] AB = CD; BF = FC [2] AB + BF = FC + CD d. [1] AB + BF = FC + CD [2] AB + BF = AF ;FC + CD = FD 7

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