Post on 23-Feb-2016
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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?