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Homework Worksheets: Chapter 7 HW#36: Problems #1-17 1.) Which of the following in an example of an 2.) Identify the converse of the given statement. undefined term: If ABC is an obtuse triangle, then it has one obtuse angle. A. ray A. If ABC has one obtuse angle, then it is an B. segment obtuse triangle. C. line B. If ABC does not have one obtuse angle, then it D. skew is not an obtuse triangle. E. angle 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. 3.) Identify a counterexample to the given 4.) A regular polygon has 10 sides. Find the sum statement. of the measures of the interior angles. All quadrilaterals are equilateral. A. square B. rectangle A. 36˚ B. 144˚ C. 360˚ C. rhombus D. hexagon D. 1440˚ E. 1800˚ E. Both A and C x 1 2x 3 6.) Similar polygons have the same______ but not 5.) If then x = x3 2x necessarily the same_________. 9 9 5 A. B. -9 C. D. A. sides; angles B. ratios; proportions 5 5 9 C. angles; sides D. proportions; ratios E. not enough information to conclude E. not enough information to conclude 7.) The given statement is true. Which other 8.) Quadrilateral ABCD is a parallelogram. If statement must be true? consecutive angles are congruent, which statement If a = b, then x y . must be true? 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 . A. ABCD is a square B. ABCD is a rectangle C. ABCD is a rhombus D. ABCD is a trapezoid E. If a = b, then x = y. E. ABCD is an isosceles trapezoid For #9-11, reduce. 2 8 5 125 3 72 9.) 10.) 11.) 4 10 6 MORE ON THE NEXT PAGE For #12-17, solve for x: 12.) 2 x 2 8 x 42 0 13.) 3x 2 75 14.) x 2 20 x 15.) 2 x 2 x 6 16.) 5 x 2 6 x 1 0 17.) 6 x 2 7 x 5 HW #37: Problems #18 - 30 18.) If ABC and XYZ are two triangles 19.) Quadrilateral MNOP is a parallelogram. Name the AB BC property of parallelograms that justifies the statement: such that , which of the NO = PM XY YZ following would be sufficient to prove that the triangles are similar? A. Opposite sides of a parallelogram are congruent. B. Opposite angles of a parallelogram are congruent. A. A X C. Diagonals of a parallelogram bisect each other. B. B Y D. Opposite sides of a parallelogram are parallel. C. C Z E. Consecutive sides of a parallelogram are congruent. D. X Y E. 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 Sum of Exterior Angles: C. two right triangles Each Exterior Angle: D. two isosceles triangles with congruent vertex Each Interior Angle: angles Sum of Interior Angles: E. not enough information to conclude For #22-24,write the equation of a line in slope intercept form given: 2 23.) Contains the points ( -2, 5) 24.) Has an x-intercept of 3 and 22.) Slope = and contains and ( 3, -4) a y-intercept of -4. 3 the point ( -6, 4) For # 25-27 Write the equation of a line in standard form given: 25.) Slope = -2 and contains the 26.) Contains the points 27.) Is perpendicular to point ( 4, -5) ( -3, 5) and ( 2, -1) 1 y x 3 and contains the 2 point ( 3, -4) For #28-30, simplify: 4 3 2 5 3 2 2 2 2 29.) 30.) 28.) 2 6 3 10 HW #38: Problems #31 – 45 31.) Given: AB and CD intersect at point E; 32.) What is the value of x in the figure? 1 2 130 A 2x C E 2 3 A. 20 4 1 B. 25 D C. 45 B 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) 34.) Which quadrilateral is equiangular but not __________ angle: equilateral? A. obtuse A. rectangle B. acute B. rhombus C. right C. square D. straight D. trapezoid E. not physically possible E. parallelogram 35.) Which of the following facts would be 36.) All of the following proportions are correct sufficient to prove that triangles ABC and DBE except: are similar? A A. CE and BE are a c a b A. B. D congruent b d c d a c B. ACE is a right angle a c d b b d C. D. C. AC and DE are d b c a C E B parallel a c D. A and B are E. ab cd congruent E. none of the above For questions 37-45, solve each using quadratic formula. 37.) 5 x 2 16 x 84 0 38.) 3x 2 39 x 108 MORE ON THE NEXT PAGE! 39.) 4 x 2 9 12 x 40.) x 2 4 x 60 41.) 4 x 2 3 x 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: 47.) Solve for b: y x 11b + 9 12a - 9 10a - 1 120 15b - 39 48.) What coordinates of A make ABCD a 49.) If a triangle has sides with lengths 12, 15, and rhombus? 20, what kind of triangle is it? y A. acute B. obtuse A B(c + 3a, 3b ) C. right D. equilateral E. None of these D(a,b) 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 51.) Pentagon FGHJK is congruent to pentagon counterexample to the assertion below: PQRST. Which side is congruent to FK ? Two lines in a plane always intersect in exactly A. PQ one point. B. QR A. coplanar lines C. ST B. parallel lines D. PT C. perpendicular lines D. intersecting lines E. none of the above 52.) A right triangle’s hypotenuse has length 5. 53.) What is the value of x in the triangle below? If one leg has length 2, what is the length of the B 10 C other leg? x x A. 2 A B. 3 C. 21 A. 5 B. 5 2 C. 10 3 D. 29 D. 10 E. 20 E. 7 MORE ON THE NEXT PAGE 54.) 55.) From which given information can you conclude that RSTW is a parallelogram? 1 l A. RS WT , RS ST 2 B. RS ST , RW WT m C. RS WT , RW ST If l m , which statement must be true? D. RZ TZ , SZ WZ A. 1 2 B. 1 is the complement of 2 C. 1 is the supplement of 2 D. 1 and 2 are right angles E. 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: ________________ For questions 1-4, find the value of the variable(s). 1. 2. (7x+37) 3y 4x (5x-10) (4x+4) (5y-80) 3. mLMN 140 4. P L (2x+2) (11x-9) (x+1) (5x+5) M N 5.) 2 and 6 are ____________________ j 1 2 angles and their measures are _______________. 4 3 If m2 7 x 6 and m6 9 x 20 , solve for x, k 5 6 m2 and m6 . 8 7 jk 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 y, m5 and m4 . a, m5 and m3 . 8.) Complete the chart for regular polygons: # of sides 6 8 Sum of exterior angles Each exterior angle 72° Each interior angle 144° Sum of interior angles 1260° 9.) Find the equation (in slope-intercept form) of 10.) Find the equation (in standard form) of the the line that has a slope of -4 and passes through line that is perpendicular to y = 2x – 5 and passes the point (-3, 1). through the point (-3, 1) 11.) In XYZ , X Y . If XZ 3a 1 , 12.) ABC is equilateral. If mA 2 x y and YZ 7 a 11 , and XY 5a , find XY. mB 4 x y , solve for x and y. 13.) PQRS is a parallelogram; solve for the 14.) A trapezoid and its median is shown. Solve variables. for x: Q R 3x + 2 a x 64 b 7 2x + 4 32 y 5 20 2x + 1 P 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 Statements A Reasons 1.) 1.) 2.) 2.) 3.) 3.) 4.) _______ _______ 4.) 5.) 5.)