Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Riemann–Roch theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Multilateration wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Geometry Honors: Chapter 2 Review Define each key word, Property, or Postulate. supplementary angles complementary angles adjacent angles linear pair vertical angles Addition Property of Equality Subtraction Property of Equality Reflexive Property Substitution Property Transitive Property Linear Pair Postulate Segment Addition Postulate Angle Addition Postulate Right Angle Congruence Theorem Congruent Supplement Theorem Congruent Complement Theorem Vertical Angle Theorem Corresponding Angle Postulate Name:____________________ Alternate Interior Angle Theorem Alternate Exterior Angle Theorem Same-side Interior Angle Theorem Same-side Exterior Angle Theorem Solve. 1. Consider the conditional statement, “If Micah’s average score is 92 or greater, then he will receive an A.” a. What is the hypothesis, p? a. b. b. What is the conclusion, q? c. What is the truth value of the conditional statement when p is false and q is true? 2. Sketch and label each of the following geometric figures. c. a. a. Two intersecting lines with vertical angles 1 and 2 and vertical angles 3 and 4 b. Name all of the linear pairs in the figure from part (a). b. c. Name the congruent angles and the supplementary angles in the figure from part (a). c. 3. The variables x and y in the figure represent the measures of angles. Solve for x and y. x y 4. Use the figure to determine the measure of each indicated angle. a. b. c. a. b. c. d. d. Proofs 5. Complete the flow chart proof by writing the Reason for each statement in the boxes provided. Given: Prove: 6. The boxes below show the parts of a flow chart proof. Rearrange the boxes (write just their number) and draw arrows to connect the boxes in a logical sequence to prove the statement. Given: , Prove: 1 4 7 2 3 6 5 8 7. Enter the Statements that complete the two-column proof below. Given: Prove: Statements a. Reasons 1. Given b. 2. vertical angles are congruent c. 3. vertical angles are congruent d. 4. Transitive Property e. 5. Transitive Property 8. Fill in the missing Statements or Reasons of the following two-column proof Given: is supplementary to , is supplementary to , and Prove: 1. Statements is supplementary to Reasons 1. Given 2. is supplementary to a. b. 3. Given 4. c. d. 5. Definition of supplementary angles e. 6. Definition of supplementary angles 7. f. g. 8. Subtraction Property of Equality h. 9. Definition of congruent angles 9. Prove the following theorem using either a flow chart or two column method. Given: Prove: Cumulative Section. Anything from the Solve Section of the Chapter 1 Test and the following two constructions: Construct (using only a compass and straightedge) the Angle Bisector of angle Construct (using only a compass and straightedge) a line perpendicular to point X. and through