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Homework Worksheets: Chapter 7 HW#36: Problems #1-17 1.) Which of the following in an example of an undefined term: 2.) Identify the converse of the given statement. A. B. C. D. E. A. If ABC has one obtuse angle, then it is an obtuse triangle. B. If ABC does not have one obtuse angle, then it is not an obtuse triangle. C. If ABC is not an obtuse triangle, then it does not have one obtuse angle. D. If ABC is an obtuse triangle, then it has one obtuse angle. E. None of the above. ray segment line skew angle If ABC is an obtuse triangle, then it has one obtuse angle. 3.) Identify a counterexample to the given statement. All quadrilaterals are equilateral. A. square B. rectangle C. rhombus D. hexagon E. Both A and C 4.) A regular polygon has 10 sides. Find the sum of the measures of the interior angles. x 1 2x 3 then x = x 3 2x 9 9 5 A. B. -9 C. D. 5 5 9 E. not enough information to conclude 6.) Similar polygons have the same______ but not necessarily the same_________. 7.) The given statement is true. Which other statement must be true? If a = b, then x y . A. If x y , then a = b. B. If a b , then x = y. C. If a b , then x y . D. If x = y, then a b . E. If a = b, then x = y. 8.) Quadrilateral ABCD is a parallelogram. If consecutive angles are congruent, which statement must be true? 5.) If A. 36˚ D. 1440˚ B. 144˚ E. 1800˚ C. 360˚ A. sides; angles B. ratios; proportions C. angles; sides D. proportions; ratios E. not enough information to conclude A. ABCD is a square B. ABCD is a rectangle C. ABCD is a rhombus D. ABCD is a trapezoid E. ABCD is an isosceles trapezoid For #9-11, reduce. 9.) 2 8 4 MORE ON THE NEXT PAGE For #12-17, solve for x: 10.) 5 125 10 11.) 3 72 6 12.) 2 x 2 8 x 42 0 15.) 2 x 2 x 6 13.) 3 x 2 75 16.) 5 x 2 6 x 1 0 14.) x 2 20 x 17.) 6 x 2 7 x 5 HW #37: Problems #18 - 30 18.) If ABC and XYZ are two triangles such AB BC that , which of the following would be XY YZ sufficient to prove that the triangles are similar? A. B. C. D. E. 19.) Quadrilateral MNOP is a parallelogram. Name the property of parallelograms that justifies the statement: NO = PM A. Opposite sides of a parallelogram are congruent. B. Opposite angles of a parallelogram are congruent. C. Diagonals of a parallelogram bisect each other. D. Opposite sides of a parallelogram are parallel. E. Consecutive sides of a parallelogram are congruent. A X B Y C Z X Y none of the above 20.) Which triangles must be similar? 21.) Find each quantity for a regular hexagon: A. two obtuse triangles B. two scalene triangles with congruent bases C. two right triangles D. two isosceles triangles with congruent vertex angles E. not enough information to conclude Sum of Exterior Angles: Each Exterior Angle: Each Interior Angle: Sum of Interior Angles: For #22-24,Write the equation of a line in slope intercept form given: 23.) Contains the points ( -2, 5) 2 22.) Slope = and contains and ( 3, -4) 3 the point ( -6, 4) 24.) Has an x-intercept of 3 and a y-intercept of -4. For # 25-27 Write the equation of a line in standard form given: 25.) Slope = -2 and contains the point ( 4, -5) 26.) Contains the points ( -3, 5) and ( 2, -1) 27.) Is perpendicular to 1 y x 3 and contains the 2 point ( 3, -4) For #28-30, simplify: 28.) 2 6 3 10 29.) 4 3 2 2 5 3 2 2 30.) 2 HW #38: Problems #31 – 45 31.) Given: AB and CD intersect at point E; 1 2 32.) What is the value of x in the figure? 130 A 2x C 3 D 2 E 4 1 B A. 20 B. 25 C. 45 D. 50 Which of the following can be used to prove that AED BEC ? A. AA B. SSS C. ASA D. SAS E. none of the above 33.) The supplement of an right angle is a(n) __________ angle: 34.) Which quadrilateral is equiangular but not equilateral? A. B. C. D. E. A. B. C. D. E. obtuse acute right straight not physically possible 35.) Which of the following facts would be sufficient to prove that triangles ABC and DBE are similar? A A. CE and BE are D congruent B. ACE is a right angle C. AC and DE are B C E parallel D. A and B are congruent E. none of the above rectangle rhombus square trapezoid parallelogram 36.) All of the following proportions are correct except: a c B. b d a c C. D. d b a c E. ab cd A. a b c d For questions 37-45, solve each using quadratic formula. 37.) 38.) 3 x 2 39 x 108 2 5 x 16 x 84 0 a b c d d b c a MORE ON THE NEXT PAGE 39.) 4 x 2 9 12 x 40.) x 2 4 x 60 41.) 4 x 2 3x 2 0 42.) 9 x 2 1 6 x 43.) 6 x 2 x 2 44.) 4 x 2 25 45.) x 2 x 0 HW#39: Problems #46 – 61 46.) Solve for x and y: y 47.) Solve for b: x 11b + 9 10a - 1 12a - 9 15b - 39 120 48.) What coordinates of A make ABCD a rhombus? y A D(a,b) B(c + 3a, 3b ) 49.) If a triangle has sides with lengths 12, 15, and 20, what kind of triangle is it? A. acute B. obtuse C. right D. equilateral E. None of these C (c, b ) x A. (a + c, 3b) B. (c, 3a + 3b) C. (4a, 3b) D. (a + c, a + b) E. (a, b) 50.) Which of the following best describes a counterexample to the assertion below: Two lines in a plane always intersect in exactly one point. 51.) Pentagon FGHJK is congruent to pentagon PQRST. Which side is congruent to FK ? A. PQ B. QR A. B. C. D. E. coplanar lines parallel lines perpendicular lines intersecting lines none of the above 52.) A right triangle’s hypotenuse has length 5. If one leg has length 2, what is the length of the other leg? C. ST D. PT 53.) What is the value of x in the triangle below? B x A. 2 B. 3 C. 21 D. 29 E. 7 MORE ON THE NEXT PAGE x A A. B. C. D. E. C 10 5 5 2 10 3 10 20 54.) 55.) From which given information can you conclude that RSTW is a parallelogram? l 1 A. RS WT , RS ST 2 m B. RS ST , RW WT C. RS WT , RW ST If l m , which statement must be true? A. B. C. D. E. D. RZ TZ , SZ WZ 1 2 1 is the complement of 2 1 is the supplement of 2 1 and 2 are right angles none of the above For #56 – 61. Solve each using the quadratic formula 56.) x 2 3x 4 0 57.) x 2 7 x 6 0 58.) x 2 4 x 2 0 59.) 4 x 2 4 x 1 60.) 3x 2 4 x 7 61.) HW#41: Midterm Review Name: ________________ 8.) Complete the chart for regular polygons: 6 # of sides Sum of exterior angles 8 For questions 1-4, find the value of the variable(s). 1. 2. (7x+37) 3y 4x (5x-10) (4x+4) (5y-80) 3. m LMN 140 4. P L (2x+2) (11x-9) (x+1) (5x+5) M N 1 j 4 5 k 8 5.) 2 and 6 are ____________________ angles and their measures are _______________. If m2 7 x 6 and m6 9x 20 , solve for x, m2 and m6 . 2 3 6 7 j k Diagram refers to #5-7 6.) 5 and 4 are _____________________ 7.) 3 and 5 are __________________ angles angles and their measures are _______________. and their measures are __________________. If If m5 13 y 23 and m4 4 y 16 , solve for m5 150 2a and m3 12a 10 , solve for a, m5 and m3 . y, m5 and m4 . 72° Each exterior angle Each interior angle Sum of interior angles 9.) Find the equation (in slope-intercept form) of the line that has a slope of -4 and passes through the point (-3, 1). 1260° 10.) Find the equation (in standard form) of the line that is perpendicular to y = 2x – 5 and passes through the point (-3, 1) 11.) In XYZ , X Y . If XZ 3a 1, YZ 7a 11, and XY 5a , find XY. 12.) ABC is equilateral. If mA 2 x y and mB 4 x y , solve for x and y. 13.) PQRS is a parallelogram; solve for the variables. 14.) A trapezoid and its median is shown. Solve for x: R Q 64 y 32 3x + 2 x a b P 144° 7 2x + 4 5 20 2x + 1 S 15.) Write the converse, inverse, and contrapositive of the statement below. Then state whether each statement is true or false. “If a quadrilateral is a square, then it has four right angles.” Converse: ________________________________________________________ True or False? Inverse: ________________________________________________________ True or False? Contrapositive: ________________________________________________________ True or False? 16.) Given: F is the midpoint of EA and DB E B Prove: A E F D A Statements Reasons 1.) 1.) 2.) 2.) 3.) 3.) 4.) _______ _______ 4.) 5.) 5.)