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Solve each proportion. Show your work. = = The figures in each pair are similar. Find the value of each variable. Show your work. Determine whether the triangles are similar. If so, write a similarity...

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  1. Solve each proportion. Show your work.
  1. =

  1. =
  1. The figures in each pair are similar. Find the value of each variable. Show your work.


  1. Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or the theorem you used. If not, explain.

b.

  1. Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.


  1. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
    1. 3in, 4in, 5 in
  1. 5in, 6in, 7in
  1. 8in, 9in, 12in
  1. Find the missing value. Show your work.


  1. Given the vertices of ?ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
    1. Rx-axis
  1. Ry = 3

  1. T<-2,5>
  1. T

  1. r(90?, o)
  1. Find the congruence transformation that maps ?ABC to ?A’B’C’. Explain your reasoning

  1. Find the area of each figure to the nearest tenth. Show your work



  1. Find the measure of each arc AB. Please make sure to show your steps.

, Where
  1. Find the area of each regular polygon. Round your answer to the nearest tenth. Show your work.
  1. Octagon with side lengths 5in.
  1. Hexagon with radius 5in

  1. Find the surface area of each figure to the nearest tenth.Show your work.




  1. What is a real-world example or use of surface area?
  1. Find the surface area of each figure to the nearest tenth. Show your work.

  1. Find the volume of each figure to the nearest tenth. Show your work.

  1. Write the standard equation of each circle

  1. Solve for x. Show your work.
  1. Evaluate. Show your work.
    1. 6!
  1. 6P5

  1. 12C3

  1. Use the spinner to find each theoretical probability
  1. P (an even number)
  2. P (a number greater than 3)
  3. P (an odd number)
  1. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.

  1. What is the area of the figure. Show your work.


005_ua5o-omxme0uh.docx
Answered Same Day Dec 27, 2021

Solution

David answered on Dec 27 2021
111 Votes
Geometry Quarter Exam

Name: ____________________________ Student Number: ____________________

Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.




1. Solve each proportion. Show your work.
a.


=


Ans: Cross multiply to get
(2x*14)=(7*12)
So x=3
.


=



Ans : Cross multiply to get
(3*7)=(5*(x-1))
21=5x-5
21+5=5x
Thus x=


2. The figures in each pair are similar. Find the value of each variable. Show your work.
a.
Using the properties of similarity we get





So 8x=16*2 so x=4
Geometry Quarter Exam

Name: ____________________________ Student Number: ____________________

Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.



.
Using the property of similarity
We get








So we get 12x=(18*4) thus x=6
Now 4y=(8*!2) thus y=24
c.
Using same angles similarity property we get








So 6x=(7*4) thus x =


and 6y=(8*4) thus y=


3. Determine whether the triangles are similar. If so, write a similarity statement and name the
postulate or the theorem you used. If not, explain.
a.
Geometry Quarter Exam

Name: ____________________________ Student Number: ____________________

Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.


Ans: As all the co
esponding angles are equal that is
Angle A =Angle P,Angle B= Angle Q and Angle C= Angle C
So these two triangles are similar by AAA theorem
.
Ans: All three pairs of co
esponding sides are in the same proportion

















So the triangles are similar by SSS theorem
Geometry Quarter Exam

Name: ____________________________ Student Number: ____________________

Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.



4. Find the value of each variable for the right triangles. Make sure all answers are in reduced radical
form. Show your work.
a.
Ans: For the triangle to be right angled
Square of the length of hypotenuse should be equal to the sum of squares of the base and
height
So here √ )=5
.
Ans: Similarly here
√ √
c.
Ans: Similarly √
Geometry Quarter Exam

Name: ____________________________ Student Number: ____________________

Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.



5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your
work.
a. 3in, 4in, 5 in
Ans: For the triangle to be right angled Square of the length of hypotenuse should be equal to the
sum of squares of the base and height
So here we can see that 52=32+42
Hence triangle is right angled.
. 5in, 6in, 7in
Ans: Here we cannot form make square of one side equal to sum of square of other
sides .Hence the triangle is not right angled.
c. 8in, 9in, 12in
Ans: Here also we cannot form make square of one side equal to sum of square of other
sides .Hence the triangle is not right angled
6. ind the missing value. Show your work.
a.
Ans: Use trigonometric relation
( )



sin(51o)=



so y=9.3257
Geometry Quarter Exam

Name: ____________________________ Student Number:...
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