Lincoln Public Schools GEOMETRY REVIEW - Semester One CALCULATOR Revised 12/2007

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1 Lincoln Public chools GOMY VIW - emester One LULO evised /007. escribe the lines in the sketch.. coplanar and intersecting. coplanar and nonintersecting. noncoplanar and intersecting. noncoplanar and nonintersecting. If m = 00, find m U is the bisector of. Find m and m U Write as a biconditional statement: If two lines are perpendicular, then they meet to form right angles.. wo lines are perpendicular if and only if they meet to form right angles.. wo lines are perpendicular if they meet to form right angles.. If two lines meet to form right angles, then they are perpendicular.. If two lines are perpendicular, then they meet to form right angles.. In symbolic notation, what is the converse of r s?. ~ r s. ~ r ~ s. s r. ~ s ~ r 9. If p q represents the statement If the traffic light is green, then you may cross the street, then ~ p ~ q represents which statement?. If you cannot cross the street, then the traffic light must not be green.. If the traffic light is not green, then you may not cross the street.. If you cross the street, then the traffic light must be green.. he traffic light must be green if you cross the street.. m = 5, m U =. m = 90, m U =. m = 04, m U = 5. m = 4, m U = 5 4. Which answer best describes how and are related?. complementary angles. linear pair of angles. supplementary angles. vertical angles 5. and are supplementary angles. If m =, find m m = 7. Find m M P O N 5 U 0. Identify the property used to complete the statement: If x 4 = 4, then x =.. ddition Property of quality. ivision Property of quality. Multiplication Property of quality. ubtraction Property of quality. How many lines through point Q are parallel to line m?. zero. one. two. infinitely many. What type of angles are and 5?. alternate exterior. alternate interior. consecutive interior. corresponding Q 7 5 m

2 . Name a line skew to... H. GH. 4. Which pair of angles are alternate exterior angles?. and 5. and. and 4. and 4 G 5 7 H F. Parallelogram and parallelogram WXYZ are congruent. Find the value of m. X Y (m + 70) (0m) What theorem or postulate is used to prove the two triangles are congruent?.... W Z 5. Name a pair of lines that must be parallel and state the reason for your conclusion.. p and q; corresponding angles are congruent.. p and q; alternate interior angles are congruent.. l and m; corresponding angles are congruent.. l and m; alternate exterior angles are congruent. p q l m 0. Find the value of x x 0. Find the measure of.. Find the measure of x x 7. olve for x x. What is the length of P? P

3 . Find.. Find the value of x. x Which of the following could be the length of? List the angles from smallest to largest..,,.,,.,,.,,. List the sides of the triangle from shortest to longest..,,.,,.,,.,, If is a parallelogram, then what are the coordinates of the midpoint of?. (, 4). (4, ). (, 0). (, ) 0. If Q is a parallelogram, then what is the m Q? If KLMN is a square, then what is the m LPM? (, 4) (, 0) K Q P L Find the value of x (x + ) (x + 0) (7x + 4). olve for x N x 0 5 M (x)

4 . Identify the polygon.. kite. parallelogram. rhombus. trapezoid If JK = KL, L is the midpoint of JM, and KL =, then what is the measure of KM?.. J K L M.. 4. Find the area of F.. 0 square units. 5 square units. 0 square units. 50 square units 5. Find the area of the trapezoid.. 4 square units. 0 square units. 0 square units. 0 square units. Find the area of the kite.. square units. square units. 44 square units. 4 square units F 5 G 40. hoose the property being illustrated: =.. istributive Property of quality. eflexive Property of quality. ymmetric Property of quality. ransitive Property of quality 4. Use the diagram to determine which statement is true.. Points W,, and V are collinear.. U uuur is perpendicular to line a.. UV and W are vertical angles.. U and UV are complementary. 4. Given the figure with m NKL = 0, find m JKM N M P 5 50 J K L 4. Which would be the correct statement for step in the proof? MN ON. and are vertical angles. Given U V W b a 7. What is the converse of the statement If I live in Lincoln, then I live in Nebraska?. If I do not live in Lincoln, then I do not live in Nebraska.. If I do not live in Lincoln, then I live in Nebraska.. If I live in Nebraska, then I do not live in Lincoln.. If I live in Nebraska, then I live in Lincoln.. Find the distance between the points (,9) and (-,) Vertical ngles heorem. and are complementary.. and are congruent.. and are supplementary.. and are a linear pair. 44. Find m 4 and m 7.. m 4 = 05, m 7 = 05. m 4 = 05, m 7 = 75. m 4 = 75, m 7 = 05. m 4 = 75, m 7 =

5 45. V uuur bisects. Find m V (x + 9) V (0x 7) 50. Find counterexample to show the following conditional statement is false. If a number is prime, then it is odd Given (,-0) and (,-), find the midpoint of.. (-,7). (,-4). (7,-). (4,-) 4. Find the value of a (4a 0) (a + 0) 5. If two angles form a linear pair, then the angles are supplementary. X and Y form a linear pair. Which conclusion represents a proper application of the Law of etachment to these statements?. X and Y are vertical angles.. X and Y have the same measure.. X and Y are complementary.. X and Y are supplementary. 47. If and are complementary and and are complementary, what is always true about and?. hey are complementary.. hey are congruent.. hey are supplementary.. hey are vertical angles. 4. Which can be used to show x // y? x 0 0 y z 5. Find the value of x lassify the triangle according to its angles.. acute. equiangular. obtuse. right (4x + ) (x + 0). If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.. If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.. If two lines are cut by a transversal so that consecutive interior angles are congruent, then the lines are parallel.. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 55. lassify the triangle according to its sides.. equilateral. right. scalene. isosceles Find the value of x. 5. Which statement is true of all rectangles? (x 40) (x + 0). iagonals are congruent.. iagonals are perpendicular.. onsecutive sides are congruent.. hey are equiangular and equilateral.

6 57. Name a pair of congruent parts using corresponding parts of congruent triangles are congruent Which of the following is always a parallelogram with perpendicular diagonals?. isosceles trapezoid. rectangle. rhombus. trapezoid. Which statement would best complete the proof? Given: Prove:, MN ON.. Given.. Given.. Vertical ngles heorem ongruence Postulate F is an obtuse isosceles triangle. Identify the relationship between angles and F.. and F are complementary angles.. and F have the same measure.. and F are a linear pair.. and F are supplementary angles. 0. Find the measure of x Find the area of the shaded region.. 4 sq. units. 4 sq. units. 9 sq. units. 0 sq. units 5 x 0 F. ngle, ide, ngle. orresponding Parts of ongruent riangles are ongruent. ide, ngle, ide. ide, ide, ide. If m 4 = 0, then which statement must be true?. m = 0. m = 0. m > 0. m < 0 4. Which segment is longest?. PQ. P. Q. PQ 4 5. he area of XYZ is 0 in and XY= 0 in. Find ZW. Z. in. in. in. 4 in P 0 Q X W Y

7 . Find m What is the slope of a line parallel to the line with equation y = x? Given m V = m V, W = W, and U. Name a median.. U. W. V. W Use the diagram for # Name three collinear points.. W,, V. W, V, P.,, P.,, V U V W W P y V x 74. What is the slope of a line perpendicular to the line with equation y = 4 x +? What is the slope-intercept equation of the line that passes through the point (5,) and is perpendicular to the line with equation y = 5 x +?. y = 5 x. y = 5 x + 0. y = - 5 x. y = - 5 x What is the slope-intercept equation of the line that passes through the point (0,) and is parallel to the line with equation y = x? 9. What is another name for line y?. P sr. W sur suur. P. PV suur. y = x +. y = x +. y = x. y = x 70. Name two opposite rays.. uuur and V uuur 7. Name two vertical angles.. uuur and W uuuur. uuur and V uuur. uuur and uuur 77. Which best describes the polygon?. equiangular. equilateral. regular. W and PV. W and WV. P and V. P and PW 7. Name one linear pair of angles.. W and PV. W and WV. P and V. P and PW 7. Which best describes the polygon?. concave, heptagon. concave, regular. convex, heptagon. convex, regular

8 OPN-N. a) ketch, with appropriate markings, one acute triangle, one right triangle and one obtuse triangle. hen sketch all three altitudes for each triangle. 79. he perimeter of rectangle is 7m. Find the value of x, the length of, and the area of.. x= 5 m = (x + ) m rea = b) rue or False: he altitudes of a triangle always meet inside the triangle. 0. a) ketch, with appropriate markings, one acute triangle, one right triangle and one obtuse triangle. hen sketch all three angle bisectors for each triangle.. is the centroid of GHJ and M =. Find H and HM. H 5. H = HM = G M J b) rue or False: he angle bisectors of a triangle always meet inside the triangle.. a) ketch, with appropriate markings, one acute triangle, one right triangle and one obtuse triangle. hen sketch all three medians for each triangle. b) rue or False: he medians of a triangle always meet inside the triangle. 4. Given: VW, WX, and XV are midsegments of, VW =, WX = 7, and = 0. Find: VX and the perimeter of.. VX = V X perimeter = 5. Given: JKLM is a parallelogram, JN = (x ) and NL = (x + 0). Find: x, JN and JL. J K (x ) 7. x = 7 W N (x + 0) JN= M L JL=

9 . Use the diagram to find each. 5 7 a) one pair of alternate exterior angles a) b) one pair of alternate interior angles b) c) one pair of consecutive interior angles c) d) one pair of corresponding angles d) 4 7. Find the slope for each pair of lines. hen label them parallel, perpendicular or neither. a) Line passes through (,) and (4,). a) Line passes through (7,) and (,5) b) Line passes through (-,) and (0,). b) Line passes through (-,-) and (,0) Matching. Match the description to the appropriate diagram. You may use some diagrams more than once. 9. scalene right triangle 90. isosceles right triangle 9. scalene triangle 9. isosceles triangle 9. complementary base angles,, 94. congruent base angles,, 95. supplementary angles,, 9. complementary angles,,..... F. # 97 0, ecide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use c) Line passes through (,0) and (,-). c) Line passes through (,5) and (7,) Use the diagram, where XYZ, to find the missing measures Z X Y m = m = m X = m Y = XZ = XY = YZ = 0. 0.

10 #0-05, ecide whether the figure is a polygon. If it is, then use the number of sides to state what kind of polygon it is #0-07, escribe the pattern and predict the next number. 0. 0,, 5, pattern: next number: 07.,,,4, pattern: next number: