Which of the following statements is/are a restatement of Euclid's Fifth Postulate? I. Through a point P not on a line I, there exists exactly one line parallel tol. II. If a line intersects one of two parallel lines, then it intersects the other. III. The sum of the angles of a triangle is at least 180°. O I only 2.2 O Il only O I and II only O I, II, II I and III only III only

Which of the following statements is/are a restatement of Euclid's Fifth Postulate? I. Through a point P not on a line I, there exists exactly one line parallel tol. II. If a line intersects one of two parallel lines, then it intersects the other. III. The sum of the angles of a triangle is at least 180°. O I only 2.2 O Il only O I and II only O I, II, II I and III only III only

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.2: Indirect Proof

Problem 11E: Which of the following statements would you prove by the indirect method? a In triangle ABC, if...

See similar textbooks

Similar questions

Which of the following statements would you prove by the indirect method? a In triangle ABC, if mAmB, then ACBC. b If alternate exterior 1 alternate exterior 8, then l is not parallel to m. c If (x+2)(x3)=0, then x=2orx=3. d If two sides of a triangle are congruent, the two angles opposite these sides are also congruent. e The perpendicular bisector of a line segment is unique.
Which of the following statements would you prove by the indirect method? a If ACAB in ABC, then mBmC. b If AC=AB in ABC, then mB=mC. c If RSTV is not a square, then RSST. d An angle has exactly one bisector.
In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false. a PandQorR b PorQandR
Complete the proof of the following theorem: In a kite, one pair of opposite angles are congruent. Given: Kite ABCD; ABADandBCDC Prove: BD PROOF Statements Reasons 1_________ 2. Draw AC 3.__________ 4. ACDACB 5.__________ 1.______________ 2. Through two points, there is exactly one line. 3. Identity 4.____________ 5._________________
Assuming that statements 1 and 2 are true, draw a valid conclusion if possible. 1 If two angles are both right angles, then the angles are congruent. 2 R and S are not congruent. C ? _________ _____________
Prove the Extended Angle Addition Property by using the Drawing, the Given, and the Prove that follow. Given: TSW with SU and SV Prove: mTSW=mTSU+mUSV+mVSW
In Exercise 1 and 2, supply reasons. Given: AB intersects CD at O so that 1 is a right Use the figure following Exercise 1. Prove: 2 and 3 are complementary. PROOF Statements Reasons 1. AB intersects CD at O. 1. ? 2. AOB is a straight , so mAOB=180 2. ? 3. m1+mCOB=mAOB 3. ? 4. m1+mCOB=180 4. ? 5. 1 is a right angle 5. ? 6. m1=90 6. ? 7. 90+mCOB=180 7. ? 8. mCOB=90 8. ? 9. m2+m3=mCOB 9. ? 10. m2+m3=90 10. ? 11. 2 and 3 are complementary 11. ?
Given: mn Transversal k m3=x23x m6=(x+4)(x5) Find: x and m4 Exercise 17-19
In Exercise 11 and 12, provide the missing statements and reasons. Given: 12;34 s 2 and 3 are complementary Prove: s 1 and 4 are complementary PROOF Statements Reasons 1. 13 and 34 1. ? 2. ? and ? 2. If two s are , then their measures are equal. 3. s 2 and 3 are complementary 3. ? 4. ? 4. The sum of the measures of complementary s is 90 5. m1+m4=90 5. ? 6. ? 6. If the sum of the measures of two angles is 90, then the angles are complementary
In Exercise 3 and 4, supply statements. Given: 12 and 23 Prove: 13 PROOF Statements Reasons 1. ? 1. Given 2. ? 2. Transitive Property of Congruence