AMSCO'S Geometry. New York - Rye High School

Postulates,Theorems, and Proof 1093. Given: LM MN 4. Given: PQR is a straight angle.Prove: LM > MNProve: mPQR 1805. Given: PQR is a straight angle. 6. Given: QP hand QR hare opposite rays.Prove: QP hand QR hare opposite rays. Prove: P, Q, and R are on the same line.7. Given: PQR is a straight angle. 8. Given: EG hbisects DEF.Prove: P, Q, and R are on the same line. Prove: mDEG mGEF9. Compare the direct proofs to the indirect proofs in problems 3–8. In these examples, whichproofs were longer? Why do you think this is the case?10. Draw a figure that represents the statement to be proved and write an indirect proof:Given: EG h does not bisect DEF.Prove: DEG is not congruent to GEF.Applying Skills11. In order to prove a conditional statement, we let the hypothesis be the given and the conclusionbe the prove.gIf BD h is perpendicular to ABC, then BD his the bisector of ABC.a. Write the hypothesis of the conditional as the given.b. Write the conclusion of the conditional as the prove.c. Write a direct proof for the conditional.12. If mEFG 180, then FE hand FG hare not opposite rays.a. Write the hypothesis of the conditional as the given.b. Write the conclusion of the conditional as the prove.c. Write an indirect proof for the conditional.3-5 POSTULATES, THEOREMS, AND PROOFA valid argument that leads to a true conclusion begins with true statements. InChapter 1, we listed undefined terms and definitions that we accept as beingtrue. We have used the undefined terms and definitions to draw conclusions.At times, statements are made in geometry that are neither undefined termsnor definitions, and yet we know these are true statements. Some of these statementsseem so “obvious” that we accept them without proof. Such a statementis called a postulate or an axiom.