Geometry Ch. 2 Review

ProofsChapter 1 Conditional Statements Constructions Proofs,

Props, Posts.

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Chapter 1– 10 Points

QUESTION:Complementary angles sum to what measure?

ANSWER:•90°

Chapter 1– 20 Points

QUESTION:Sketch & label:

Points F, R, and G are collinear and R is the midpoint of .

ANSWER:

Chapter 1– 30 Points

QUESTION:• and are supplementary. If and , classify ? (hint: finding the measure first would be a good start…)ANSWER:

• is obtuse

Chapter 1– 40 Points

QUESTION: H bisects . If and , what is the value of ?

ANSWER:

Chapter 1– 50 PointsQUESTION:

An angle is ten less than four times its complement. What are the measures of the angles?

ANSWER:

Conditional Statements– 10 PointsQUESTION:

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.

Conditional Statements– 20 PointsQUESTION:Identify the hypothesis & conclusion in the statement:

Goldie will win the tournament if she beats Joy.

ANSWER: Hypothesis: Goldie beats JoyConclusion: Goldie will win the tournament

Conditional Statements– 30 PointsQUESTION: 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.

Conditional Statements– 40 PointsQUESTION: 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.

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 and are vertical, then and are .

ANSWER:Contrapositive: If and are not , then and are not vertical. (TRUE)Biconditional: and are vertical IFF and are .

(FALSE and don’t have to touch)

Constructions– 10 PointsQUESTION: Name the two tools used in geometric constructions.

ANSWER: Compass and straightedge

Constructions– 20 PointsQUESTION:

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.

Constructions– 30 PointsQUESTION:Which construction is shown below?

ANSWER:Perpendicular Bisector

Constructions– 40 Points

QUESTION:Draw an obtuse angle and copy it (construction).

ANSWER:

Constructions– 50 PointsQUESTION:Construct a 45 degree angle.

ANSWER:Perpendicular bisector, angle bisector.

Proofs– 10 PointsQUESTION:

What is the property illustrated below:

ANSWER:Symmetric Property

Proofs– 20 PointsQUESTION:

What is the definition that would be a reason for the following:

therefore .

ANSWER:Definition of congruent segments

Proofs– 30 Points

QUESTION:Provide a reason for the statement below:

ANSWER:•Substitution

Angle Add. Post.

?????

Proofs– 40 PointsQUESTION: Toby needs help writing a proof to show that . Complete his proof.

Statements Reasons1. is a straight angle;, 1.

2. 2. Angle Add. Post.3. 3. 4. 4. Simplify5. 5. 6. 6. 7. 7. Substitution8. 8. Simplify

Proofs– 50 PointsQUESTION: Prove the following:If and , then

𝟏𝟐

Statements Reasons1. 1. 2. 2. Vertical Angles Thm.

3. 3. 4. 4. 5. 5. 6. 6. 7. 7. Division Prop. =8. 8. 9. 9.

Topic 5 – 10 Points

QUESTION:

• This isometric transformation would not result in AA’ parallel to BB’.

ANSWER:

• What is a rotation?

Topic 5 – 20 Points

QUESTION:

• These are the three isometric transformations we studied.

ANSWER:

• Reflection, Translation and Rotation.

Topic 5 – 30 Points

QUESTION:

• In this transformation, no point will ever remain in the same position.

ANSWER:

• What is a translation?

Topic 5 – 40 Points

QUESTION:

• 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?

Topic 5 – 50 Points

QUESTION:

• 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?