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1st Semester Exam Review Chapter 1: Vocabulary Plane Angle Bisector Segment Bisector Segment Opposite Rays Line Postulate Midpoint Congruent Segments Supplementary Angles Congruent Acute Angle Linear pair of angles Vertical Angles Adjacent Angles Coplanar Hypotenuse Right Angle Vertex Obtuse Angle Collinear Complementary Angles Problems Match each type of angle to its diagram. ________ 1. Straight ________ 2. Obtuse ________ 3. Right ________ 4. Acute a. b. c. Find each length. 5. 7. AB = BD = 6. 8. AD = A B C D –5 –2 0 2 BC = 9. Find AB given B is between A and C. 10. Find m ABC given m ABD = 78 . 11. Solve for x. M is the midpoint. 12. BC is a bisector for ABD . Solve for x if mABD = 5x 4 and mABC 2x 5 = . 13. M is the midpoint of LN . L has coordinates (–3, –1), and M has coordinates (0, 1). Find the coordinates of N. 15. Find the midpoint of 4,3 & 2, 7 . 14. Find the length of AB, with coordinates A(1, –2) and B(–4, –4) 16. Find the distance between (–4, 3) & (–2, –7). Leave your answer in radical form. 17. An angle measures 3 times its supplement. Find the 18. E is the midpoint of measure of the angle and its supplement. Use the diagram to name each of the following: 19. A plane _________ X C● D● ● ●A 20. A line ___________ B B DF , DE = 2x + 4, and EF = 3x – 1. Find DE, EF, and DF. Use the diagram to name each of the following: 24. Name a pair of vertical angles ______________ 25. Name a linear pair 21. Opposite rays ______ ______ 22. 3 collinear points _____ _____ _____ ______________ 26. Name a pair of adjacent angles ___________________ 27. Name a pair of complementary angles 23. A segment containing point A ________ ____________________ Chapter 2: Vocabulary Inductive Reasoning Hypothesis Converse Biconditional Statement Conjecture Conclusion Inverse Polygon Counterexample Truth Value Contrapositive Triangle Conditional Statement Negation Deductive Reasoning Quadrilateral Problems Make a conjecture about the each pattern. Write the next two items. 1. __________________________ 2. ___________ ___________ 1 1 1 1 , , , ,... 3 6 12 24 ______________________________ ________ ________ Complete the conjecture. 3. The sum of an even number and an odd number is _______________. 4. A product of an integer and its reciprocal is _______________. Determine whether the conjecture is true or false. If it is false, give a counterexample. 5. An even number plus 3 is always odd. 6. A prime number plus 3 is always even. True……False True……False 7. For any three points in a plane, there are three different lines that contain two of the points. True……False Determine if the conditional statement is true. If it is false give a counterexample. 8. If two angles are obtuse, then they are 9. If a pair of angles form a linear pair, then they supplementary. are supplementary. True……False True……False 10. If two angles are adjacent, then they have a common ray. True……False Given the conditional statement “If the measure of 1 is 105, then 1 is obtuse,” write the converse, inverse and contrapositive, find the truth value of each. 11. converse: ______________________________________________________________ T……F 12. inverse: _______________________________________________________________ T……F 13. contrapositive: __________________________________________________________ T……F 14. Write a conditional statement from the sentence: “A rectangle has congruent diagonals.” ___________________________________________________________________________ 15. Write the converse and a biconditional statement for the conditional: “If a number is divisible by 10, then it ends in 0.” converse: _____________________________________________________________________ biconditional: __________________________________________________________________ 16. Determine if the biconditional “The sides of a triangle measure 3, 7, and 15 if and only if the perimeter is 25 in.” is true. If false, give a counter example. ______________ ___________________________________________________________ 17. Write the definition as a biconditional. “Parallel lines are coplanar lines that never intersect.” ___________________________________________________________________________ 18. Identify the hypothesis and conclusion of the conditional statement. Underline the hypothesis once and the conclusion twice. “Two angles are supplementary angles if the sum of their measures is 180. 19. Write a conditional statement from the following. “Sixteen-year-olds are eligible to drive.” 20. Determine if the biconditional, “A number is divisible by 6 if and only if it is divisible by 3” is true. If false, give a counterexample. 21. Solve for x and justify each step: 4x – 5 = 2 Statement Reason 22. Solve for x and justify each step: 3 x 2 x 2 Statement 23. Solve for x and justify each step: x 2 Statement Reason 2x 8 5 Reason 24. If GH has coordinates G (2, 6) and H (-1, -1) find the distance of GH. Justify each step Statement Reason 25. If M is the midpoint of AB and A has coordinates (-1, 0) and M has coordinates (5,4). Find point B. Justify each step. Statement Reason 26. QS bisects PQR, mPQR = (6x - 4), and mSQR = (2x + 4). What is the value of x? Justify each step. Statement Reason 27. D is between C and E. CE = 6x, CD = 2x + 3, and DE = 13. Find CE. Justify each step. Statement Reason Chapter 3: Vocabulary Parallel Lines Transversal Same-side Interior angles Perpendicular Lines Corresponding Angles Perpendicular Bisector Skew Lines Alternate Interior Angles Slope Parallel Planes Alternate Exterior Angles Problems Use figure 1 to name to following: 1. Name all segments skew to WX 2. Name all segments parallel to QR 3. Name all segments perpendicular to PS 4. Name a plane parallel to plane WPS 5. Name a corresponding angle to 4 6. Name a same-side interior angle to 6 7. Name an alternate exterior angle to 2 8. Name an alternate interior angle to 4 Transversal Classify the Pair of Angles 9. 4 and 6 10. 6 and 7 11. 2 and 3 EF DG . Find the measure of each angle. 12. m ABE 13. m EBC Use figure 5 to find the value of x and y. a 14. b c a 6x + 5y 54 b 62 x ____________ c 6x + 3y y ____________ figure 5 15. Solve for x and y in figure 6. E 8x + 4y 7x + 6y D F x ____________ 84 G figure 6 y ____________ a) Which theorem could be used to show a b when: b) Find the angle measure. 16. 1 3 17. 7 + 6 = 180° m 1 = (21x + 1) and m 3 = (30x – 44) m 7 = (12x – 8) and m 6 = (5x + 18) a) b) a) b) 8 1 2 7 3 6 4 5 figure 7 18. Complete the proof of the alternate exterior angles theorem using figure. Given: r s Prove: 1 2 s 2. Reason 1. 13 3 2 Statement 1. 1 r 2. 3. 3. Vertical Angle Thm. 4. 4. figure 8 23 1+2=3 Reflexive Prop of Transitive Prop of Corresponding Thm Addition Prop of 19. Name the shortest segment, write an inequality for x, then solve the inequality. 20. Lines p and q together contain a linear pair in which the angles are congruent. What is the relationship between lines p and q? __________, _______________, ___________ Determine if line r is parallel to line t based on the given information. If yes, state the theorem or postulate that justifies your conclusion. 21. 1 3 Yes / No ____________________________ t r 22. 4 6 Yes / No ____________________________ 1 2 3 4 23. m 3 + m 8 = 180 Yes / No 5 6 8 7 ____________________________ Find the value of x that makes line r parallel to line t. Use the figure above. 24. m 3 = 8x – 7 & m 7 = 3x + 8 25. m 2 = 7x + 10 & m 5 = 11x – 64 Using the points, graph each pair of lines. Then use the slope formula to determine whether the lines are parallel, perpendicular, or neither. 26. 27. JK & JL, J 4, 2 , K 4, 2 , L 4,6 AB & CD A 2, 1 , B 3, 4 C 2, 3 , D 3, 6 ______________ ___________ Write the equation for each line. 28. Write the equation of the line with slope 2 3 29. Write the equation of the horizontal line passing through (2, 3) in point-slope form. passing through (6, –4) in point-slope form. 30. Write the equation of the line passing through 31. Write the equation of the line with (5, 2) and (–2, 2) in slope-intercept form. y-intercept –3 and x-intercept 4 in slope-intercept form. Graph each line. 32. y = 2 33. y 4 2 ( x 6) 3 34. y 3 x 4 35. y 4 x Determine whether the lines are parallel, intersecting, or coinciding. 36. y x 7 5 37. y x 4 y x 3 38. x + 2y = 6 1 y x 3 2 2 2y 5 x 4 39. 7x + 2y = 10 3y 4 x 5 Chapter 4: Vocabulary Acute Triangle Equilateral Triangle Corresponding Angles Included Side AAS Vertex Angle Equiangular Triangle Isosceles Triangle Corresponding Sides SSS HL Base Right Triangle Scalene Triangle Congruent Polygons SAS CPCTC Base Angles Obtuse Triangle Remote Interior Angle Included Angle ASA Legs of an Isosceles Triangle Problems Problems Classify the following triangles by angles and sides 1. 2. 123 3. 23 67 Sketch RAD BIG . Label all sides and angles to represent their congruence, then complete the following congruency statements. 4. 5. Sketch the two triangles here: G ________________ AD __________________ 6. IGB ________________ 7. GB ________________ Solve for the missing angle measures or missing variables. 8. 9. 10. A 10x + 20 D 5x + 80 C mD ________________ mP ________________ t=________________ AC _____________________ 11. (3x + 5) 12. 2x 13. (2x + 10)° (3x – 5)° x ________________ mO __________________ x ________________ mO __________________ mPRS = __________________ 14. 15. 16. (2x + 3)° 77° 168° x = __________________________ x = ______________________ mS= ___________________ w = ______________________ TS = _______________________ 17 – 25: State whether each pair of triangles is congruent by SSS, SAS, ASA, AAS, or HL. If possible, write a congruence statement for each pair of triangles. If the triangles are not congruent write “Not ” in the blank and list any additional information you would need to be able to say the triangles are congruent. 17. 18. 19. Q Y Z P X 20. 21. R 22. P L O N Q 23. 24. 25. F E G H Determine if you can prove the two triangles congruent using the given information. If they are congruent state the theorem or postulate that justifies your answer. If there is not enough information, write none. 27. VS bisects RST and RVT 26. G W, MA HO , M H M H _____________________ ________________ W O A G 28. An acute angle in a right triangle has a measure of 3 10 . Find the measure of the other acute angle. 4 29. In a right triangle, the measure of one acute angle is 31°. Find the the measure of the other acute angle. 30. Given: FGHI is a rectangle FI GH , FIH and GHI are right angles Prove: FH GI STATEMENTS REASONS 1. FGHI is a rectangle 1. 2. FI GH , FIH and GHI are right angles 2. 3. 3. Rt Thm 4. 4. Reflexive Prop of 5. FIH GHI 5. 6. 6. 31. The angles of a triangle are in the ratio 5:12:13. Find the measure of each angle. 32. Write the equation of the line with slope of –6 and y intercept –8 in slope intercept form. 34. Write the equation of the line passing through (5, 1) 35. Write the equation of the perpendicular bisector to the line passing through (6,0) and (0,4) in slope intercept form. and (8, –2) in point slope form. Simplify the following radical expressions. 350 1. 162 2. 156 3. 4. 7 40 5. 12x 3 y 8 z 2 6. 6 25x y z 4 4 3 2 25 44 2 13. 9 3c 44 11. 10 3 15c 14. c5 d 2 e f 4 24 6 6 2 12. 3 12 c 0 e 6f 4 0 2 30 15. 4 c d e f 7 4 1 2 c 0 e 5f 0 16. 4 18. 441 17. 2 5 8 125 6 19. 11 517 2 1 81 20. 22. 29 24. 21. 2 x 5t 2 81t 3 23. 54t 7 65 x 2 25. 9 196 87 2 9 a4b6 81t 3 108t 7 64a 2