Geometry Final ExamStudy Guide – PART 1

  1. Point S is on . If ,, and, find the value of x.
  1. T is the midpoint of . If and , find the length of PT.
  1. bisects∠XYZ. If and , what is the ?
  1. ABD and DBC form a linear pair. If and , what is the value of y?
  1. Sally and Johanna want to play on Saturday. Sally’s house is at S(-2,3) and Johanna’s house if at J(6,-9) on the map. If the park is in the exact middle of their houses, where would the park be located?
  1. If the endpoint of a segment is P(5,-2) and the midpoint is M(0,8), find the other endpoint, Q.
  1. and2 are complimentary angles. If , what is the ?

Use the figure to the right to answer #8-12.

  1. Name a set of vertical angles.
  2. Name a pair of same side interior angles.
  3. Name a set of alternate interior angles.
  4. Name a set of alternate exterior angles.
  5. Name a set of corresponding angles.

13. Use the diagram at right to answer the questions below.

a. What is the value of x?

b. What is the measure of ACD?

For #14-15, find the value of x if and .16. In the diagram below, find .

14.15.

16.

  1. In isosceles , and are the base angles and is the vertex angle. If and , what is the value of x?
  1. What is the slope of a line perpendicular to ?
  1. What is the equation of a line parallel to that contains the point (4,-1)?
  1. What rule describes a translation of 6unitsright and 2 units down?

Use the diagram at right for #22-24

  1. What kind of transformation describes ABC A’B’C’?
  2. If ABC was dilated by a scale factor of 4 what would be the image of A?
  3. If ABC was reflected across the y-axis, what would be the image of C?

For #25-26, which postulate or theorem, if any, could you use to prove the two triangles congruent?


  1. In the diagram at right, the triangles are congruent because of SSS.

Write a congruence statement to describe the triangles.

  1. Using the diagram below, find the 28. List the sides of the triangle from shortest to longest.

value of x.

  1. A triangle has one side that is10 cm long and another side that is 7 cm long. What could be the length of the third side?
  1. is an equilateral triangle. If , what is the value of x?
  1. What is the sum of the interior angles in a decagon (10 sides)?
  1. What is the measure of an exterior angle of a heptagon (7 sides)?
  1. List the characteristics of a parallelogram.
  1. List the hierarchy of quadrilaterals.
  1. Find the measurements of angles 1, 2, and 3. 36. Find the measurements of angles 1 and 2.

Use the diagram at right for questions 38-39.

  1. Find the value of x.
  2. What is the measure of
  1. What is the midsegment of the trapezoid at right?
  1. Solve for x:
  1. Members of the school band are buying pots of tulips and pots of daffodils to sell at their fundraiser. They plan to buy 121 pots of flowers. The ratio of tulips to daffodils is 5:6. How many pots of daffodils should they buy?
  1. The length of a rectangular playground in a scale drawing is 7 in. If the scale is 2 in = 5ft, what is the actual length of the playground?
  1. A 2-ft vertical post casts a 18 inch shadow at the same time a pine tree casts a 80ft shadow. How tall is the pine tree?

Are the triangles similar? How do you know?

  1. 45.
  1. Are the figures in the diagram below similar? If they are, write a similarity statement and give the scale factor.
  1. Find the values of x and y. Leave your 48. Find the value of x in the diagram below.

answers in simplest radical form.

  1. Find the values of x and y if the two figures are similar.
  1. Find the hypotenuse of a right triangle if the legs are 13 in and 9 in long. Leave your answer in simplest radical form.
  1. Find the value of x in the diagram below. Use the properties of 30-60-90 and

Leave your answer in simplest radical form.45-45-90 triangles to solve #21-52.

Leave your answers in simplest radical form.

51. 52.

For questions #53-54, use trigonometry to find the value of x in each diagram.

  1. 54.
  1. A woman stands 20ft from a statue. She looks up at an angle of 55° to see the top of the statue. Her eye level is 5.5ft from the ground. How tall is the statue to the nearest foot?
  1. A triangle has the following side lengths: 7 cm, 9 cm, 12cm. What kind of triangle is it (acute, right, or obtuse)?

For #57-61, find the area of the figure.

  1. Trapezoid
  1. Kite
  1. Rhombus
  2. Parallelogram
  3. Equilateral Triangle

Find the volume for each figure below:

  1. 65. 66. 67.

Use the figure at right for #64-66.

  1. What is the ?
  2. What is the arc length of ?
  3. What is the area of Sector APB?

For #67-70, find the value of the variable.


Use the diagram at the right for #75-77

  1. What is the value of a?
  1. What is the value of b?
  1. What is the value of c?
  1. What is the equation of a circle that has a center at (0,4) and had a radius of 7?

Use the equation to answer questions 79-80.

  1. What is the center of the circle?
  1. What is the radius of the circle?
  1. In an airplane flying 5 miles over the ocean, the pilot looks down at an 18° angle of depression and spots an island. To the nearest mile, what is the horizontal distance to the island.

  1. Use the law of sines to find the value of x in the diagram below. Round to the nearest whole number.