Geometry Fall Final Exam Review THIS IS A CLASS SET! PLEASE DO NOT WRITE ON.
1. Complete the composite transformation. Rotate
the figure 90° and then translate the
triangle (𝑥, 𝑦) → (𝑥 + 2, 𝑦 − 3).
2. Complete the composite transformation. Rotate
the figure 90° and then translate the figure
(𝑥, 𝑦) → (𝑥 + 1, 𝑦 − 5)
4. A polygon with vertices
(2,2), (6,2), (6,4), 𝑎𝑛𝑑 (4,6). Rotate the
polygon 180° and state the new coordinates.
3. A polygon with vertices
(1,1), (3,1), (3,2), 𝑎𝑛𝑑 (2,3). Rotate the
polygon 180° and state the new coordinates.
5. Which triangles are congruent?
6. Which composition of transformations maps
triangle ABC to triangle A’B’C’?
a. Translation (𝑥, 𝑦) → (𝑥, 𝑦 + 3)
Reflection over 𝑥 = −1
b. Translation (𝑥, 𝑦) → (𝑥 + 1, 𝑦 + 3)
Reflection over 𝑥 = −1
c. Translation (𝑥, 𝑦) → (𝑥 + 3, 𝑦)
Reflection over 𝑦 = −1
d. Translation (𝑥, 𝑦) → (𝑥 + 3, 𝑦 + 1)
Reflection over 𝑦 = −1
7. Suppose ∆𝐴𝐵𝐶 ≅ ∆𝐾𝑅𝐿, ∆𝐾𝑅𝐿 ≅
∆𝑃𝑄𝑆, 𝑚∠𝐿 = 115°, 𝑚∠𝐴 = 33°. What is the
𝑚∠𝐾?
8. Suppose ∆𝐴𝐵𝐶 ≅ ∆𝐾𝑅𝐿, ∆𝐾𝑅𝐿 ≅
∆𝑃𝑄𝑆, 𝑚∠𝐿 = 110°, 𝑚∠𝐴 = 50°. What is the
𝑚∠𝐾?
9. Find the value of x.
10. Find the value of x.
51°
11. What does it mean to have rotational symmetry? Provide an example of shape that does have rotational
symmetry AND a shape that does not have rotational symmetry.
12. Which shape does not have rotational symmetry?
a.
b.
13. Triangle ABC is reflected over the x axis. If
triangle ABC has coordinates (1, 1), (2, 1), and
(1, 2), what is the coordinates of the new
image?
c.
d.
14. Triangle ABC is reflected over the x-axis. If
triangle ABC has coordinates (3, 3), (6, 3), and
(3, 6), what is the coordinates of the new
image?
15. Describe the angles in a right triangle. (Hint: explain the biggest angle and the other two angles)
16. State if the three numbers can be the measures
of the sides of a triangle.
7, 5, 4
17. State if the three numbers can be the measures
of the sides of a triangle.
3, 6, 2
18. State all the congruent angles. (Hint: have three groups of congruent angles)
19. What are the coordinates of the vertices of the image after the composition of transformations shown below
for ∆𝐴𝐵𝐶 with vertices A(1, 1), B(1, 2), and C(2,1).
Translation: (𝑥, 𝑦) → (𝑥 + 4, 𝑦 − 1)
Rotation: 90° about the origin
20. What are the coordinates of the vertices of the image after the composition of transformations shown below
for ∆𝐴𝐵𝐶 with vertices A(-2, 0), B(1, 1), and C(-1,2).
Translation: (𝑥, 𝑦) → (𝑥 + 4, 𝑦 − 1)
Rotation: 90° about the origin
21. ̅̅̅̅
𝐴𝐵 has an endpoint (2, 5) and a midpoint at
(3,4). What is the length of ̅̅̅̅
𝐴𝐵?
22. ̅̅̅̅
𝐴𝐵 has an endpoint (4, 15) and a midpoint
at (6, 12). What is the length of ̅̅̅̅
𝐴𝐵?
23. Determine if the following deductive argument is valid or invalid:
A person who lives in Florida lives in the United States.
Mickey Mouse lives in the Unites States.
Therefore, Mickey Mouse lives in Florida.
24. Determine if the following deductive argument is valid or invalid:
Since all robins have two legs, and since all birds are two-legged, it follows that all robins are birds.
25. In the figure, ∠𝑃𝑆𝑅 ≅ ∠𝑅𝑆𝑄. What is
the value of 𝑥 𝑖𝑓 ∠𝑃𝑆𝑅 = (8𝑥 + 11)° and
m∠𝑅𝑆𝑄 = 75°?
26. In the figure, ∠𝑃𝑆𝑅 ≅ ∠𝑅𝑆𝑄. What is
the value of 𝑥 𝑖𝑓 ∠𝑃𝑆𝑅 = (2𝑥 + 4)° and
m∠𝑅𝑆𝑄 = 80°?
27. In the figure, m∠𝑄𝑅𝑆 = 80°. What is
the m∠𝑃𝑅𝑄?
28. In the figure, m∠𝑄𝑅𝑆 = 60°. What is
the m∠𝑃𝑅𝑄?
29. Write an equation that is parallel to the
line 𝑦 = 3𝑥 + 4 and passes through the
point P (9, -2).
30. Write an equation that is passes
through point P and is perpendicular to the
line in the given equation. 𝑃 (12, 4)
𝑦 = 6𝑥 + 6
31. Write an equation that is parallel to the
1
line 𝑦 = 2 𝑥 + 5 and passes through the
point P (6, -7).
32. Write an equation that is passes through point
P and is perpendicular to the line in the given
equation.
𝑃 (2, 4)
1
𝑦 = 2𝑥 + 2
33. Find the value of x.
34. Find the value of x.
35. If given the slopes of the sides of a polygon. Explain how you would know that two sides were
parallel, perpendicular, or not related.
36. Write an equation of the perpendicular
bisector of the line segment whose
endpoints are (-1,4) and (7, 0).
37. Write an equation of the perpendicular
bisector of the line segment whose
endpoints are (-1, -3) and (1, 5).
38. Find the midpoint of the segment with endpoints (1,2) 𝑎𝑛𝑑 (5,10).
39. ̅̅̅̅
𝐶𝐷 has an endpoint (4, 10) and a midpoint at (6, 8). What is the coordinate of the other endpoint?
40. Find the value of x and y.
41. Find the value of x.
42. What are the coordinates of point C in right triangle ABC?
A(3,7) and B(2,1)
a. C(9,6)
b. C(5,4)
43. What is the scale factor of the given dilation?
𝐴(3, −3) 𝐵(6,9) 𝐶(12, −3)
𝐴′ (1, −1)𝐵′ (2,3)𝐶′(4, −1)
Given that DE is a mid-segment of the triangle, solve for n.
44.
45.