Homework Worksheets Chapter 7 - PDF by vww89216

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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 =
      x3      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




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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.      
                                                                                  ab cd
                       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




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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.   mLMN  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 m2  7 x  6 and m6  9 x  20 , solve for x,
         k             5 6                         m2 and m6 .
                  8     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 m5  13 y  23 and m4  4 y  16 , solve for m5  150  2a and m3  12a  10 , solve for
y, m5 and m4 .                                  a, m5 and m3 .




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 mA  2 x  y and
YZ  7 a  11 , and XY  5a , find XY.               mB  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.)

								
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