Geometry Ch. 2 Review Created by Educational Technology Network. www.edtechnetwork.com 2009

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

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 𝐹𝐺 . ANSWER:

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

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

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°

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.

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

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.

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.

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)

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

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.

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

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

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

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

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

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 ?????

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. 3. 2𝑛+ 6𝑛−4 =180 3. 4. 4. Simplify 5. 6. 𝑛=23 6. 7. 7. Substitution 8. 8. Simplify

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.

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

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

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

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?

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?