G. Tawfik          
MATHEMATICS 436

Extra-Review 9A Geometry: Similarity
                          See:  Extra-Review 9 A  Practice Sheet  #2
                               Notes on Similarity
                                      Notes about Angles
                                      Notes about Area and Volume of Solids



1.   Given the two right triangles shown
      DB = 6,  AB = 9  and AC = 12,
      find the measure of CF.
                   



2.    In the diagram shown,
       DE = 3 cm    AE = 4 cm   BC = 9 cm

       a.   Prove that the two right triangles shown
              are similar.

       b.   Determine the measures of sides:
               AD,   AB   and   AC.

       c.   What is the ratio of the areas of these
             triangles?


                





3.    In the diagram shown,  
        AC = 4,  CD = 6, 
        CE = 5   BC = x
        and  AB is parallel to DE.
   
       Determine the value of x.
         




4.    Sides XY and BC are parallel.

    a.    Find the value of XY if AY : YC = 4 : 3  
           and BC = 42 cm.

    b.    What is the ratio of the areas of
            these triangles?
               



5.    If the length of the sides of one triangle is triple the length of the sides of another triangle,
       find the ratio of their areas.


6.    The ratio of the areas of triangle ABC and triangle DEF is 25 : 9.

    a.    Determine the ratio of the sides of these triangles.

    b.    If the height AH of triangle ABC measures 6 units, what is the measure of the corresponding
           height DK of the other triangle?


7.    The sides of triangle GHI are 3 cm, 5 cm and 7 cm.
       Find the sides of a similar triangle JKL which has an area 9 times that of triangle GHI.


8.    A pair of corresponding sides of two similar triangles measures 5 cm and 8 cm, respectively.
       The area of the larger triangle is 20 cm2, find the area of the smaller triangle. 




9.    The areas of two similar triangles are 36 cm2 and 64 cm2, respectively.

    a.    Find the ratio of a pair of corresponding medians in these triangles.

    b.    What is the ratio of the perimeter of these triangles?


10.    The sides of two equilateral triangles measure 4 cm and 7 cm, respectively.

          a.    What is the ratio of their altitudes?

          b.    What is the area of each triangle?

          c.    What is the ratio of the areas of these triangles?





11.    If the ratio of the areas of two similar triangles is
         9 : 16, what is the length of side AB of the smaller
         triangle, if the corresponding side DE of the larger
         triangle measures 10 cm?




Answers

1.    CF = 8


2.    AD = 5    AB = 15    AC = 12


3.    BC = 4,8


4.    XY = 24                   Area AXY    =  16
                                        Area ABC        49
   

5.        Area small   =   1
             Area big          9


6.      AB    =    5                DK = 3,6
         DE          3
   

7.    Sides large triangle:  9,  15,   21


8.    Area small triangle = 7,8 cm2  


9.    Median small   =    3                Perimeter small  =    3
         Median big           4                  Perimeter big          4

         
10.    Side small   =      4                Area small = 3,46                    Area small   =    16   =  0,33
           Side big             7                   Area big = 10,61                     Area big          49


11.    AB = 7,5