Name: 2015 Midterm Review Period: Date:


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1 GEOMETRY Name: 2015 Midterm Review Period: Date: To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the following chapters. Use this guide to help you practice. UNIT 1 (Chapter 2 Logic): Conditional Statements (Converse, Inverse, Contrapositive, Biconditional) Inductive/Deductive Reasoning UNIT 2 (Chapter 1 Essentials of Geometry and Constructions): Points, Lines and Planes Segments and Congruence Midpoint and Distance Formulas Measure and Classify Angles Describe Angle Pair Relationships Construct Congruent Segments/Angles, Segment Bisector, Perpendicular Bisector, Angle Bisector UNIT 3 (Chapter 3 Parallel Lines): Parallel Lines and Angle Relationships (Corresponding, Consecutive, Alternate Interior/Exterior) Perpendicular Lines Find and Use Slopes of Lines Write and Graph Equations of Lines Construct Parallel Lines UNIT 4 (Chapters 4/5 Triangles: Intro/Congruence/Inequalities): Triangle Classification (Acute, Obtuse, Right, Equiangular, Equilateral, Scalene, Isosceles) Triangle Sum Properties Isosceles and Equilateral Triangle Properties Inequalities in a Triangle Relationships Between Side Lengths and Angle Measures Triangle Congruence (SSS, SAS, AAS, ASA, HL) Proofs UNIT 5 (Chapter 6 Similarity): Ratios and Proportions Similarity in 1D/2D/3D Prove Triangles are Similar (AA, SSS, SAS) Proportionality Theorems
2 UNIT 1 (Chapter 2 Logic): 1. Consider the following legend: Let p = You love pie. Let q = You see stars. Let r = You have spots. Express the following in words. q p p ~r ~q r q p p r 2. Write the sentence as a conditional statement in ifthen form in words. Write the converse, inverse, and contrapositive in words. State the truth value (whether it s true or false) for each. If it s false, write a counterexample. All dogs have ears. Conditional: Converse: Inverse: Contrapositive: 3. Determine if the argument is valid or invalid. If the argument is valid, write which law(s) of logic (Law of Detachment, Law of Syllogism, or Law of the Contrapositive) makes the argument valid. c d c d p q a ~ b ~ r s p ~ q d e d e A) q ~ r B) b c C) s t D) E) F) p e f e f p ~ r a c t r ~ q f c ~ f ~ c 4. According to the Venn Diagram shown, which of the following statements are true? If the statement is false, change the first word to make it true. a) All rectangles are parallelograms. b) Some parallelograms are rectangles. c) Some rectangles are rhombuses. d) Some squares are rectangles. e) No rhombuses are squares. f) No parallelograms are trapezoids. g) Some trapezoids are quadrilaterals.
3 UNIT 2 (Chapter 1 Essentials of Geometry and Constructions): Use the graph of PQRS to answer # Find the midpoint of SP. Write the coordinates. 6. Find the length of SP. Write your answer as a simplified radical and rounded to the nearest tenth. 7. Let M be the midpoint of RS Find the length of MS. 8. Let M(6, 2) be the midpoint of AB. If the coordinates of A are (3, 4), find the coordinates of B. Use a straightedge and compass to construct the following: 9. Bisect AB and label the midpoint M. Then construct segment CM through the given point C. 10. Construct a line perpendicular to line p through point N. A B 11. Using a straightedge and compass, bisect ABC with BD to create ABD & DBC. Then, using the ray provided, construct an angle that is congruent to either ABD or DBC. A B C
4 UNIT 3 (Chapter 3 Parallel Lines): 12. Find the measure of the following angles and variables given that only m k. m 1 = m 2 = m 3 = m 4 = m 5 = x = y = 13. Find x, y, and z. x = y = z = 14. Given m 1 = (6x + 20) o and m 2 = (4x + 50) o. Find the measure of 1. Are j and k parallel? Explain why or why not. m 1 = j & k parallel? (Y/N): Why? k j 15. a) Find the slope of the given line and write its equation. b) Plot and label the point B (4, 4). Write the coordinates of two other points that lie on a line perpendicular to line a and passing through point B. c) Plot and label the point C (2, 1). Write the coordinates of two other points that lie on a line parallel to line a and passing through point C. Equation of line a: Points on the line perpendicular: and a Points on the line parallel: and 16. Construct a line parallel to line p through point N.
5 UNIT 4 (Chapters 4/5 Triangles: Intro/Congruence/Inequalities): In the figures below mark any additional angles or sides that you know are congruent just from the given information. Name the congruent triangles (or NEI) and state the postulate/theorem that proves the 2 triangles are congruent V P S H 24. Given: AB DC and AD BC Prove that AD CB Statements Reasons List the sides and angles in order from smallest to largest. Prove your answer by showing all necessary measurements A W S Is it possible to construct a triangle with the given side lengths? Explain , 5, , 6, , 10, 2 Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. Write your answer with words and as an inequality in., 9 in.
6 UNIT 5 (Chapter 6 Similarity): 31. Solid A (shown) is similar to Solid B (not shown) with the given scale factor of A to B. Find the surface area and volume of Solid B. Scale Factor of 5:2 32. Some information about the volumes and surface areas of two similar prisms is given. Prism A s volume is 54 cubic feet. Prism B s volume is 16 cubic feet and its surface area is 12 square feet. Find the surface area of Prism A. 33. Corresponding lengths in similar figures are given. Find the unknown area. Can the two triangles be proved similar? If so, write the similarity statement and postulate/theorem Find the value of x
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