Geometry Midterm Review Spring 2011 Name Date Period. 2. Name three points that are collinear Name a pair of opposite rays. 3.

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1 Name Date Period Unit 1 1. Give two other names for AB Name three points that are collinear Name a pair of opposite rays Give another name for CD. 4. Point J is between H and K on HK. Use the given information to write an equation in terms of x. Solve the equation. Then find HJ and JK Find the distance between the points. Leave answer in simplest radical form The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent Page 1 of

2 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse, right, or straight. 13. AFB 14. BFD AFC 16. AFE Roof trusses can have several different layouts. The diagram below shows one type of roof truss made out of beams of wood. Use the diagram to identify two different examples of the indicated type of angle pair. In the diagram HBC and BCE are right angles. 17. Supplementary angles Complementary angles Vertical angles Linear pair angles 20. Tell whether the figure is a polygon. If it is not, explain why. If it is a polygon, tell whether it is convex or concave The perimeter of a rectangle is 690 inches and its length is 213 inches. 25. Find the width of the rectangle. Page 2 of 18

3 26. You are planting grass on a square plot of land. You are also building a fence around the edge of the plot. The side length of the plot is 54 yards. a. How much area do you need to cover with grass seed? 26a. b. How many feet of fencing do you need? 26b. 27. You make a window out of a rectangular pane of glass by surrounding it with a wooden frame that is x inches wide. The pane of glass is 20 inches long and 24 inches wide. The perimeter of the 2 window is 8 feet. What is the value of x Find the circumference of the circle. 28. Round your answer to the nearest tenth. Use the diagram below. Tell whether the angles are vertical angles, a linear pair, or neither and and and and Page 3 of 18

4 Solve for the values of x and y x = y = 34. x = y = x = y = 36. x = y = Unit 2 Draw the next figure in the pattern The first three objects in a pattern are shown. How many gray squares are in the next object? Write the next number in the pattern. Describe the pattern in the numbers , 224, 335, 446, 6. 4, 6, 9, 13, 18, pattern: pattern: 7. 1, 4, 9, 16, 8. 2, 5, 11, 23, pattern: Page 4 of 18 pattern:

5 Rewrite the given statements below in conditional (if-then) form. Underline the hypothesis, and circle the conclusion. 9. It is time for dinner if it is 6 p. m. 10. There are 12 eggs if the carton is full. 11. An obtuse angle is an angle that measures more that 90 and less than The car runs when there is gas in the tank. Write the converse, inverse, and contrapositive of each statement below: 13. If you like hockey, then you go to the hockey game. Converse: Inverse: Contrapositive: 14. If x is odd, then 3x is odd. Converse: Inverse: Contrapositive: Write the converse of each true statement. If the converse is also true, combine the statements to write a true bi-conditional statement. 15. If an angle measures 30, then it is acute. Converse: Bi-conditional (if applicable) 16. If two angles are supplementary, then their sum if 180. Converse: Bi-conditional (if applicable) Page 5 of 18

6 True or False 17. Three noncollinear points determine a plane Any three points lie on a distinct line Through any two points, there exists exactly one line A line contains at least two points. 20. Write the property that completes the statement Use the diagram at the right to solve for the indicated angles. Label the angle measure Solve for x. 29. W Z 30. FG = JH Page 6 of 18

7 Solve for x Unit 3 Think of each segment in the diagram as part of a line. Complete the statement with parallel, skew, or perpendicular Classify the following angles as corresponding, alternate interior, alternate exterior, consecutive (same side) interior, or no relation and and Page 7 of 18

8 Find the value of x that makes m // n Find the slope of the line that passes through the given points. 17. (1, 2) and (7, 7) 18. (3, 4) and (-5, 0) (5, -2) and (5, 8) 20. (3, 1) and (-5, 3) Identify the slope of the line that would be parallel to the given line. 21. y = 5 3x 22. 4x + 2y = y 5 = 3( x 2) Identify the slope of the line that would be perpendicular to the given line. 24. y = 2x x y = y + 2 = 5( x 6) Page 8 of

9 Determine which of the following lines, if any, are parallel or perpendicular Write an equation of the line that passes through the given points. 29. (-1, 0), (0, -2) 30. (0, 4), (6, 13) (4, 5), (8, 2) 32. (-1, -9), (6, 5) Find the measures of the following angles: Page 9 of 18

10 Graph each equation Unit 4 Find the values of the missing variables Page 10 of 18

11 Find the values of the variables Find the perimeter of the triangle P = 12. In DEF if DE EF and m D is 43, then m F is? In XYZ if XY YZ and m Y = 52, then m Z is?_ In DOG if O G, DO = 2x + 3, OG = 2x, and DG = 9, then x is _?_ In CAT if C A, CA = 7, and AT = 4, then CT is _?_. 15. If TJM PHS, then 16. P? JM? MT =? HPS? 19. Page 11 of 18

12 Is the given information enough to prove the triangles congruent? If so, write a congruence statement and state the theorem or postulate to justify your reasoning Yes or No 21. Yes or No 22. Yes or No 23. Yes or No ABD STR MAE ADK State the third congruence that is needed to prove that DEF QRT using the given postulate or theorem. 24. Given that D Q, F T, then by the AAS Congruence Theorem. 25. Given that E R, EF, RT, then by the ASA Congruence Theorem. 26. Given that DE QR, D Q, then by the SAS Congruence Theorem. 27. Given that DE QR, FD TQ, then by the SSS Congruence Theorem. Unit 5 Given BD is the perpendicular bisector of AC and m A = 52, 1. Classify the triangle Solve for x Solve for m C. 4. Solve for m CBA Page 12 of 18

13 Is it possible to construct a triangle with the given side lengths? If not, explain why not. 5. 3, 4, 5 5. Y or N 6. 1, 4, 6 6. Y or N 7. 17, 17, Y or N 8. 22, 26, Y or N Describe the possible lengths of the third side of the triangle given the lengths of the other two sides inches, 9 inches feet, 12 feet meters, 18 meters yards, 16 yards 12. In each of the following triangles tell whether BD is a perpendicular bisector, angle bisector, median, or altitude. List all that apply C Solve for the indicated variable given the proportion. B D A Page 13 of 18

14 Given similar polygons, corresponding angles are? corresponding sides are? corresponding perimeters are? Corresponding parts can be determined by? 24. The polygons below are similar as indicated. Find the value of x E D 27. A rectangle has a length of 6 meters. A similar rectangle is drawn using a scale 27. of 1:4. What is the length of the second rectangle? 28. You have two equilateral triangles. The scale factor is 3:2. The side length of 28. the first triangle is 6 centimeters. What is the side length of the second triangle? In the diagram, XYZ MNP , Page 14 of 18

15 The two triangles are similar. Find the values of the variables Given ABC PQR, solve for x. 36. Given RST XYZ, solve for a Determine whether there is enough information to determine triangles similar. If so, by what postulate? Page 15 of 18

16 Solve for the indicated variable Page 16 of 18

17 Solve for the indicated variable Unit 6 Find the indicated variable. Figures are not drawn to scale. Round your answers to the nearest tenth x x x 8. x Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as acute, right, or obtuse. Be sure to show your work. 5. 5, 7, , 9, , 12, , 30, 34 Page 17 of 18

18 Find the missing side lengths in the following triangles: x y y x in x y 45 x y x y Page 18 of 18

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