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Geometry Ch. 2 Review

Geometry Ch. 2 Review. 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. Chapter 1– 10 Points. QUESTION:

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Geometry Ch. 2 Review

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  1. Geometry Ch. 2 Review

  2. 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 . • ANSWER:

  5. Chapter 1– 30 Points • QUESTION: • and are supplementary. If and , classify ? • (hint: finding the measure first would be a good start…) • ANSWER: • is obtuse

  6. Chapter 1– 40 Points • QUESTION: • H bisects . If and , what is the value of ? • ANSWER:

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

  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 and are vertical, then and are . • ANSWER: • Contrapositive: If and are not , then and are not vertical. (TRUE) • Biconditional: and are verticalIFF and are . • (FALSE and 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: • What is the property illustrated below: • ANSWER: • Symmetric Property

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

  20. Proofs– 30 Points • QUESTION: • Provide a reason for the statement below: • ANSWER: • Substitution

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

  22. Proofs– 50 Points QUESTION:Prove the following: If and , then

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

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

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

  26. 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?

  27. 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?

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