1. Geometry Ch. 2 Review
Created by Educational Technology Network

2. Conditional Statements
Chapter 1
Conditional Statements
Constructions
Proofs, Props, Posts.
Proofs 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50

3. Chapter 1– 10 Points QUESTION:
Complementary angles sum to what measure?
ANSWER:
90°

4. Chapter 1– 20 Points QUESTION: Sketch & label:
Points F, R, and G are collinear and R is the midpoint of 𝐹𝐺 .
ANSWER:

5. Chapter 1– 30 Points QUESTION: ANSWER:
∠𝐷𝐸𝐹 and ∠𝐹𝐸𝐺 are supplementary. If m∠𝐷𝐸𝐹=9𝑥+1 and m∠𝐹𝐸𝐺=8𝑥+9, classify ∠𝐷𝐸𝐹?
(hint: finding the measure first would be a good start…)
ANSWER:
∠𝐷𝐸𝐹 is obtuse

6. Chapter 1– 40 Points QUESTION: ANSWER:
H bisects 𝑊𝑌 . If 𝑊𝑌=4𝑥−6 and 𝐻𝑌=5, what is the value of 𝑥?
ANSWER:
𝑥=5

7. Chapter 1– 50 Points QUESTION: ANSWER:
An angle is ten less than four times its complement. What are the measures of the angles?
ANSWER:
20°, 70°

8. Conditional Statements– 10 Points
QUESTION:
Write the statement below as a conditional statement:
Jack will fall if he fetches the water.
ANSWER:
If Jack fetches the water, then he will fall.

9. Conditional Statements– 20 Points
QUESTION:
Identify the hypothesis & conclusion in the statement:
Goldie will win the tournament if she beats Joy.
ANSWER:
Hypothesis: Goldie beats Joy
Conclusion: Goldie will win the tournament

10. Conditional Statements– 30 Points
QUESTION:
Consider the statement:
If it is Sunday, then Chloe visits her grandma.
It is Sunday.
Make a conjecture and name the law that supports your conjecture.
ANSWER:
Chloe will visit her grandma; the Law of Detachment.

11. Conditional Statements– 40 Points
QUESTION:
Is the conjecture Valid or Invalid?
If a polygon has three sides, then it is a triangle. If a triangle has a 90 degree angle, then it is a right triangle.
Conjecture: If a polygon has three sides, then it is a right triangle.
ANSWER:
Invalid—misapplication of the law of syllogism.

12. Conditional Statements– 50 Points
QUESTION:
Write the contrapositive and the biconditional form of the statement below. State whether each is true or false (if false, give a counterexample)
If ∠𝐴 and ∠𝐵 are vertical, then ∠𝐴 and ∠𝐵 are ≅.
ANSWER:
Contrapositive: If ∠𝐴 and ∠𝐵 are not ≅, then ∠𝐴 and ∠𝐵 are not vertical. (TRUE)
Biconditional: ∠𝐴 and ∠𝐵 are vertical IFF ∠𝐴 and ∠𝐵 are ≅.
(FALSE ∠𝐴 and ∠𝐵 don’t have to touch)

13. Constructions– 10 Points
QUESTION:
Name the two tools used in geometric constructions.
ANSWER:
Compass and straightedge

14. Constructions– 20 Points
QUESTION:
Jerry is in the process of doing the angle bisector construction. His work is shown below. What should be his next step?
ANSWER:
Create a ray starting at the vertex, through the intersection of the arcs.

15. Constructions– 30 Points
QUESTION:
Which construction is shown below?
ANSWER: Perpendicular Bisector

16. Constructions– 40 Points
QUESTION:
Draw an obtuse angle and copy it (construction).
ANSWER:

17. Constructions– 50 Points
QUESTION:
Construct a 45 degree angle.
ANSWER:
Perpendicular bisector, angle bisector.

18. Proofs– 10 Points QUESTION: ANSWER: Symmetric Property
What is the property illustrated below:
𝑎=𝑏, 𝑏=𝑎
ANSWER:
Symmetric Property

19. Proofs– 20 Points QUESTION: ANSWER: Definition of congruent segments
What is the definition that would be a reason for the following:
𝐴𝐵 ≅ 𝑀𝑁 therefore 𝐴𝐵=𝑀𝑁.
ANSWER:
Definition of congruent segments

20. Proofs– 30 Points QUESTION: ANSWER: Substitution
Provide a reason for the statement below:
ANSWER:
Substitution
𝑚∠𝐷𝐹𝐺+𝑚∠𝐺𝐹𝐻=𝑚∠𝐷𝐹𝐻
Angle Add. Post.
2𝑛+ 6𝑛−4 =180
?????

21. Proofs– 40 Points
QUESTION: Toby needs help writing a proof to show that 𝑚∠𝐷𝐹𝐺=46°. Complete his proof.
Statements
Reasons
∠𝐷𝐹𝐻 is a straight angle;
𝑚∠𝐷𝐹𝐺=2𝑛, 𝑚∠𝐺𝐹𝐻=6𝑛 1.
2. 𝑚∠𝐷𝐹𝐺+𝑚∠𝐺𝐹𝐻=𝑚∠𝐷𝐹𝐻
2. Angle Add. Post.
𝑛+ 6𝑛−4 =180 3. 4.
4. Simplify 5.
𝑛=23 6. 7.
7. Substitution 8.
8. Simplify

22. Proofs– 50 Points QUESTION: Prove the following:𝟏 𝟐
QUESTION: Prove the following:
If 𝑚∠1=5𝑥+70 and 𝑚∠2=12𝑥+35, then 𝑚∠1=95°
Statements
Reasons 1. 2.
2. Vertical Angles Thm.
3. 𝑚∠1=𝑚∠2 3.
4. 5𝑥+70=12𝑥+35 4. 5. 6. 7.
7. Division Prop. = 8. 9.

23. Topic 5 – 10 Points QUESTION: ANSWER:
This isometric transformation would not result in AA’ parallel to BB’.
ANSWER:
What is a rotation?

24. Topic 5 – 20 Points QUESTION: ANSWER:
These are the three isometric transformations we studied.
ANSWER:
Reflection, Translation and Rotation.

25. Topic 5 – 30 Points QUESTION: ANSWER:
In this transformation, no point will ever remain in the same position.
ANSWER:
What is a translation?

26. Topic 5 – 40 Points QUESTION: ANSWER:
If I reflect a figure across y = 4 and then across y = 9, this is the result.
ANSWER:
What is a translation up 10 units?

27. Topic 5 – 50 Points QUESTION: ANSWER:
If I reflect a figure across both lines that intersect at a 64 degree angle, this is the result.
ANSWER:
What is a rotation of 128 degrees?