Geometry EOC Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Geometry EO Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Show that the conjecture is false by finding a counterexample. If, then. a., c., b., d., 2. Write a conditional statement from the statement. horse has 4 legs. a. If it has 4 legs then it is a horse. c. If it is a horse then it has 4 legs. b. Every horse has 4 legs. d. It has 4 legs and it is a horse. 3. Fill in the blanks to complete the two-column proof. Given: and are supplementary. m = Prove: m = 45 Proof: Statements Reasons 1. and are supplementary. 1. Given 2. [1] 2. Given 3. m + m = m = Substitution Property 5. m = a. [1] m = 135 efinition of supplementary angles Subtraction Property of Equality b. [1] m = 135 efinition of supplementary angles Substitution Property c. [1] m = 135 efinition of supplementary angles Subtraction Property of Equality d. [1] m = 135 efinition of complementary angles Subtraction Property of Equality 4. Give an example of corresponding angles.

2 a. and c. and b. and d. and 5. Identify the transversal and classify the angle pair and. n m l a. The transversal is line l. The angles are corresponding angles. b. The transversal is line l. The angles are alternate interior angles. c. The transversal is line n. The angles are alternate exterior angles. d. The transversal is line m. The angles are corresponding angles. 6. Find m. R >> S (3x)º T U (4x 24)º >> V a. m = c. m = b. m = d. m =

3 7. Use the information, and the theorems you have learned to show that. 1 l 2 m a. y substitution, and. y the Substitution Property of Equality,. y the onverse of the lternate Interior ngles Theorem,. b. y substitution, and. Since and are alternate interior angles,. y the onverse of the Same-Side Interior ngles Theorem,. c. y substitution, and. Since and are same-side interior angles,. y the onverse of the Same-Side Interior ngles Theorem,. d. Since and are same-side interior angles, and. y substitution,. y the onverse of the lternate Interior ngles Theorem,. 8. Write and solve an inequality for x. 2x a. c. b. d. 9. Use the slope formula to determine the slope of the line.

4 10 y x a. 0 c. b. d. undefined Use slopes to determine whether the lines are parallel, perpendicular, or neither. 3 2 a. neither c. parallel b. perpendicular 11. One of the acute angles in a right triangle has a measure of. What is the measure of the other acute angle? a. c. b. d. 12. Find and, given,, and. N F E P M a., c., b., d., 13. Given: Identify all pairs of congruent corresponding parts.

5 M O N a.,,,,, b.,,,,, c.,,,,, d.,,,,, 14. Given that and m = 23, find m. E 23º a. m = 77 c. m = 23 b. m = 67 d. m = Given:,,. T is the midpoint of. R S Prove: T U omplete the proof. Proof: Statements Reasons Given 2. and are right angles. 2. [1] Right ngle ongruence Theorem Given Given

6 7. T is the midpoint of. 7. Given efinition of midpoint efinition of congruent triangles a. [1] efinition of right angles Third ngles Theorem Transitive Property of ongruence b. [1] efinition of perpendicular lines Third ngles Theorem Reflexive Property of ongruence c. [1] efinition of perpendicular lines Vertical ngles Theorem Symmetric Property of ongruence d. [1] efinition of perpendicular lines Third ngles Theorem Symmetric Property of ongruence 16. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles. Given:,,, Prove: E omplete the proof. Proof: Statements Reasons 1.,, 1. Given Given [1] efinition of congruent triangles a. [1] Reflexive ngles Theorem Third ngles Theorem b. [1] Third ngles Theorem Vertical ngles Theorem c. [1] Vertical ngles Theorem Third ngles Theorem d. [1] Vertical ngles Theorem Third ngles Theorem 17. Given the lengths marked on the figure and that bisects, use SSS to explain why.

7 E 4 cm 4 cm 3 cm 3 cm a. c. b. d. The triangles are not congruent. 18. The figure shows part of the roof structure of a house. Use SS to explain why. R S T U omplete the explanation. It is given that [1]. Since and are right angles, by the Right ngle ongruence Theorem. y the Reflexive Property of ongruence,. Therefore, by SS. a. [1] c. [1] b. [1] 19. Show for. d. [1] 6a - 2 a + 7 4a omplete the proof... by the Reflexive Property of ongruence. So by [5].

8 a. [1] 16 [4] 16 [5] SS b. [1] 26 [4] 26 [5] SSS c. [1] 16 [4] 16 [5] SS d. [1] 16 [4] 16 [5] SSS 20. Use S to prove the triangles congruent. Given:,, Prove: HGF G > >> F >> > H omplete the flowchart proof. Proof: Given 1. HGF Given 2. S Given a. 1. lternate Exterior ngles Theorem 2. lternate Interior ngles Theorem b. 1. lternate Interior ngles Theorem 2. lternate Exterior ngles Theorem c. 1. lternate Exterior ngles Theorem 2. lternate Exterior ngles Theorem d. 1. lternate Interior ngles Theorem 2. lternate Interior ngles Theorem

9 21. etermine if you can use the HL ongruence Theorem to prove need to know.. If not, tell what else you P ^ ^ Q a. Yes. b. No. You do not know that and are right angles. c. No. You do not know that. d. No. You do not know that. 22. Given:, bisects Prove: ) F ) G omplete the flowchart proof. Proof: Given 1. bisects 2. Given. efinition of angle bisector

10 a. 1. ongruent omplements Theorem Transitive Property of ongruence 4. PT 5. S b. 1. ongruent Supplements Theorem Transitive Property of ongruence 4. S 5. PT 23. Find. c. 1. ongruent Supplements Theorem Reflexive Property of ongruence 4. S 5. PT d. 1. ongruent omplements Theorem Reflexive Property of ongruence 4. PT 5. S ) s + 2 ) 2 s 10 ) a. = 10 b. = 12 c. = 14 d. Not enough information. n equiangular triangle is not necessarily equilateral. 24. Find the value of x. Express your answer in simplest radical form. x 3 6 a. x = c. x = b. x = d. x = 25. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27" TV screen?

11 height 27" width a. width: 21.6 in., height: 16.2 in. c. width: 21.6 in., height: 5.4 in. b. width: 16.2 in., height: 21.6 in. d. width: 5.4 in., height: 21.6 in. 26. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain a. The missing side length is 15. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation. b. The missing side length is The side lengths do not form a Pythagorean triple because one of them is not a nonzero whole number. c. The missing side length is 5. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation. d. The missing side length is The side lengths form a Pythagorean triple because they satisfy the equation. 27. Find the value of x. Express your answer in simplest radical form. 5 x x a. c. x = b. x = d. x = x = 28. Find the values of x and y. Express your answers in simplest radical form.

12 24 30º y 60º x a., c., b., d., 29. The Yield sign has a shape of an equilateral triangle with side length of 36 inches. What is the height of the sign? Will a rectangular metal sheet of inches be big enough to make one sign? a. The Yield sign is about 33.7 inches tall. So the rectangular metal sheet will not be big enough to make one sign. b. The Yield sign is about 31.2 inches tall. So the rectangular metal sheet will be big enough to make one sign. c. The Yield sign is about 25.5 inches tall. So the rectangular metal sheet will be big enough to make one sign. d. The Yield sign is about 50.9 inches tall. So the rectangular metal sheet will not be big enough to make one sign. 30. Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. a. polygon, decagon c. polygon, dodecagon b. polygon, hexagon d. not a polygon 31. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. a. regular and concave c. regular and convex b. irregular and concave d. irregular and convex

13 32. MNOP is a parallelogram. Find MP. M N 5x 3x+12 P O a. MP = 25 c. MP = 20 b. MP = 30 d. MP = Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth. Y 15 9 X 12 Z a. cos X = c. cos X = b. cos X = d. cos X = 34. Use a special right triangle to write tan 60 as a fraction. a. c. b. d. 35. Use your calculator to find the trigonometric ratios sin 79, cos 47, and tan 77. Round to the nearest hundredth. a. sin 79 = 0.99, cos 47 = 0.44, tan 77 = b. sin 79 = 0.44, cos 47 = 0.99, tan 77 = c. sin 79 = 0.68, cos 47 = 0.98, tan 77 = 4.33 d. sin 79 = 0.98, cos 47 = 0.68, tan 77 = Use the trigonometric ratio to determine which angle of the triangle is. 1.3 cm cm 0.5 cm a. 2 c. 3 b. 1 d. No solution.

14 37. Use your calculator to find the angle measures degree. a. = 44.4, = 72.5, = 88.5 b. = 0.8, = 1.3, = 1.5 c. = 1.3, = 0.8, = 1.5 d. = 72.5, = 44.4, = 88.5 to the nearest tenth of a

15 Geom. EO review nswer Section MULTIPLE HOIE 1. NS: Pick values for a and b that follow the condition if the conjecture holds.. Then substitute them into the second inequality to see Values of a and b a > b onclusion Let and. The conjecture holds. Let and. The conjecture holds. Let and. The conjecture is false. and is a counterexample. The conjecture is false when a is positive and b is negative. Feedback orrect! In this case, a/b is greater than zero, so it is not a counterexample. In this case, a is not greater than b. The counterexample should have a > b and a/b less than or equal to 0. In this case, a is not greater than b. a > b is the condition of the conjecture. The counterexample should have a > b and a/b less than or equal to 0. PTS: 1 KEY: inductive reasoning counterexample 2. NS: Identify the hypothesis and conclusion. Hypothesis horse If it is a horse, onclusion has 4 legs. then it has 4 legs. Feedback Identify the hypothesis and conclusion. conditional statement should have a hypothesis and a conclusion. orrect! conditional statement should have a hypothesis and a conclusion. PTS: 1 3. NS: Proof: KEY: conditional statement if-then hypothesis conclusion Statements Reasons