Chapter 6 Review Geometry Name________________________________ Score _______ Period ___ Date ________  

Solve  the  proportion.  

1. 1

3−m

=43

5−m

m = __________ 2. n12 =

3n n = __________

Find  the  geometric  mean  of  the  two  numbers.     Copy  and  complete  the  statement.  

3. 12 and 6 _____________ 4.    If  97 =

yx , then

x7 =

?? __________  

     5.    Is  NPQR  similar  to  VUTS  ?    _________  

         If  yes,  Explain  why  ________________________________          6.    ∆PQR  is  similar  to  ∆LMN.      

 a)    Find  the  scale  factor  of  ∆PQR  to  ∆LMN  ________________  

   

b)    Find  the  value  of  x.     c)    Find  the  value  of  y.       d)    Find  the  value  of  z        x  =  _____________          y  =  ____________          z  =  ____________            

     7.    Find  the  length  of  RQ.    _________________        8.    Find  the  value  of  y.       y  =  _________________  

             9.    Are  the  triangles  to  the  right  similar?    _________      

 If  yes,  a)  Explain  why  _________________________________  

 and    b)  Write  a  similarity  statement  ___________________            

10.    Are  the  triangles  to  the  right  similar?    _________      

   

If  yes,  a)    Explain  why  _________________________________  

and    b)  Write  a  similarity  statement  ___________________      

   11.    Find  the  value  of  a.     a  =  ________________                  12.    A  rectangular  swimming  pool  has  dimensions  of  30  ft  wide  and  50  ft  long.    The  rectangular    

 fence  around  the  pool  is  similar  to  the  shape  of  the  pool.    The  fence  is  45  ft  wide.    Find  the  length  of  the  fence.  

Length  =     __________________    

12

x 4

A

B

C D

E

18

     13.    Find  the  value  of  x.       x  =  ________________    

Chapter 7 / Review Pythagorean theorem: c2 = a2 + b2 , where a and b are the measures of the length of the 2 legs of the right triangle and c is the measure of the hypotenuse. 1. What is the longest side of a right triangle called? _____________________ 2. What is the length of the hypotenuse of a right triangle with leg lengths of 3 in. and 4 in.?

A. 5 inches B. 9 inches C. 16 inches D. 25 inches

3. Find the length of r. r = _________ 4. Find the length of h. h = _________  

5. Find the height and the area of the isosceles triangle below.

h = ______________

Area = ___________

Using the converse of the Pythagorean theorem If the square of the longest side is equal to the sum of the squares of the 2 other legs of the triangle, then the triangle is a right triangle. 6. Is ∆PYT a right triangle? (yes/no) = _________

7. Classify the triangle formed by the side lengths 14, 21, and 25 as acute, right, or obtuse.

_____________ The geometric mean between 2 numbers is the square root of their product. x = ab , where a and b are the 2 numbers and x is the geometric mean. Find the geometric mean of the following pairs of numbers. a. 4, 9 b. 16, 5 c. 12, 16

Theorem 7-2: If an altitude is drawn from one vertex of a right angle of a right triangle to its hypotenuse, then the 2 triangles formed are similar to the given triangle and to each other. The measure of this altitude is the geometric mean between the measures of the two segments of the hypotenuse. Moreover, the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg. Practice the examples below and apply these theorems. 8. Identify the three similar right triangles in the diagram to the right. ∆________∼ ∆________∼ ∆________

9. Find the length of x. x = __________ 10. Find the length of x. x = __________ ===================================================== A 45-45-90 triangle is the only isosceles right triangle. The hypotenuse is 2 times as long as a leg, so the ratio of the sides is 1:1: 2 . A 30-60-90 triangle also has special properties. The measures of the sides are x, x 3 , and 2x, giving the sides a ration of 1: 3 :2. If you see these special triangles, you do not have to use the Pythagorean theorem to find the sides of the right triangle. 7.4 Find the value of each variable. 1. 2. 3. 4. 5.

7.5 Find tan A and tan B. Write each answer as a fraction. You might want to use, SOH CAH TOA, to remember the trigonometric ratios of the sides of a triangle given an angle. These ratios help you find angles and sides of a right triangle. 6. 7. Use a tangent ratio to find the value of x. Round your answer to the nearest tenth. 8. 9. 7.6 Use a sine or cosine ratio to find the value of each variable. Round to nearest tenth. 10. 11. 7.7 Solve a right triangle by finding all the angles and sides of the triangle given. Round your answer to the nearest tenth. Remember that to find the angles, you must use the trigonometric inverses. When you use your graphing calculator, use the second button before you press the cos, sin, or tan. 12. 13.  

14.    A  30-­‐‑foot  tree  casts  a  12-­‐‑foot  shadow.  Find  the  angle  of  elevation  from  the  end  of  the  shadow  on  the  ground  to  the  top  of  the  tree  (to  the  nearest  tenth  of  a  degree).                  

Angle  of  Elevation  =  ____________  

Chapter 8 / Review 1. What is the sum of the measures of the exterior angles of an octagon? 1. _____________ 2. What is the sum of the measures of the interior angles of a decagon? 2. _____________ 3. The sum of the measures of the interior angles of a polygon is 720º. 3. _____________ How many sides does the polygon have? 4. Find the value of x. x = _____________ 5. Find the value of x. x = _____________ 6. Find the value of x. x = _____________ 7. Find the value of x and y. x = ___________ y = ___________ 8. Find the value of x and y. x = _________ 9. Find the value of h and k. h = ________ y = _________ k = ________ 10. Find the value of x and y. x = _________ y = _________

11. Find the value of x and y. x = ________ y = ________

12. Find the measures of ∠L, ∠J, ∠M. ∠L = _______ ∠J = _______ ∠M = _______ 13. Find the value of x. x = _________ 14. Find the measures of ∠V and ∠T. ∠V = _________ ∠T = _________  True  or  False  13.    Diagonals  are  congruent  in  a  rectangle  and  a  square.   13.    ___________

14.    All  angles  are  congruent  in  a  square  and  a  kite.   14.    ___________    

15.    All  sides  are  congruent  in  a  parallelogram.     15.    ___________    

16.    Base  angles  are  congruent  in  an  isosceles  trapezoid.   16.    ___________    

17.    All  angles  and  sides  are  congruent  in  a  rhombus.   17.    ___________    

18.    Diagonals  bisect  each  other  in  a  parallelogram.                  18.    ___________

Chapter 10 Review Geometry Name ____________________________________ Period ______ Date ____________ Use the diagram to match the notation with the term that best describes it. 1. ___________ 2. ___________ 3. ___________ 4. ___________ 5. ___________ 6. ___________ 7. ___________ 8. Find the value of x. _________ 9. Find the value of r. _________

(Point B and D are points of tangency)              10. ACand BEare diameters of circle F. Find the measure of the arcs:     a.       =    __________   c.         =    __________         b.       =    __________   d.         =    __________  

    11. Find the value of x. _________ 12. Find the value of x. _________      

13. The measure of arc AC = 150 º 14. Find the measure of ________ Find the measure of arc AB ________

 

15. Find the measure of ∠LNM _________ 16. Find the measure of x and y. x = ______ Find the measure of arc LN __________ y = ______ 17. Line t is tangent to the circle. 18. Find the value of x. _________

Find the measure of ___________

19. Find the value of x. _________ 20. Find the value of x. _________

21. Find the value of x. _________ 22. Find the value of x. _________

Chapter 11 Review Geometry Name ________________________________ Period ______ Date _________  

For each problem, write the area formula and show all of your work. Make sure to label your answer with the appropriate unit of measure.

1. Find the area. ___________ 2. Find the area. ___________

3. Find the area. ___________ 4. Find the area. ___________

5. Find the area. ___________ 6. Area = 415 ft2. h = _________

3 9 f t

h 2 4 f t

7. Area = 120 ft2 x = _________ 8. Area = 24 yd2 x = _________

9. ∆JKL ∼ ∆XYZ Find the length of side XY ______________

9 ft.

x

10. The ratio of the areas of two trapezoids is 81:25. Write the ratio of the lengths of the corresponding sides. ___________ 11. Find the circumference of a circle with radius 5.5 inches. __________________

12. Find the area of a circle with radius 8.1 ft. __________________

13. Find the diameter of a circle with C = 74 ft. __________________

14. Find the arc length of AB. __________ 15. Find the length of radius AQ. __________ 16. Find area of the shaded sector. _________ 17. Find area of the regular polygon. _________ 18. Find the probability that a point W, selected randomly on PQ, is on the segment PR. _____________ 19. Find the probability that a randomly selected point lies on the shaded region. _____________

3.3 4

Chapter 12 Review For Final 1. Find the number of faces, vertices, and edges of the polyhedron below. Faces ________ , Vertices ________, Edges ________ 2. Find the surface area. ____________ 3 . Find the surface area. ____________

4. Find the surface area. ___________ 5. Surface Area = 717 in2 . Find x. __________ 6. Find the volume. ____________ 7. Find the volume. ____________ 8. Find the volume. ____________ 9. Volume = 72 ft3. Find x. __________

10. Find the surface area and volume. S = _____________ V = _____________ 11. Determine whether the solids below are similar. Be sure to explain your answer. _________________________________________ 12. Solid A (shown) is similar to Solid B (not shown). The scale factor is 1: 3. Find the surface area S and volume V of Solid B. S = _____________

V = _____________