Book I. Propositions 29 and 30Problems Back to Proposition 29. 11. State Postulate 5. To see the answer, pass your mouse over the colored area. If a straight line that meets two straight lines makes the interior angles on the same side less than two right angles, then those two straight lines, if extended, will meet on that same side. 12. a) State the hypothesis of Proposition 29. Two straight lines are parallel. 2. b) State the partial conclusion. A straight line that meets them makes the alternate angles equal. 2. c) Practice Proposition 29 up to that conclusion. 13. Name four ways of knowing that two angles are equal. They are corresponding angles of congruent triangles. They are vertical angles. When a straight line meets two parallel lines, they are the alternate angles. They are right angles. 14. Complete the proof of Proposition 29; use the conclusion that the 14. a) If two straight lines are parallel, then a straight line that meets them makes Apply the enunciation to the figure, and prove it.
Let the straight lines AB, CD be parallel, and let the straight line EF meet them;
For, since the straight lines AB, CD are parallel, 3. b) If two straight lines are parallel, then a straight line that meets them makes Apply the enunciation to the figure, and prove it. The proof follows
Let the straight lines AB, CD be parallel, and let the straight line EF meet
them;
For, to each of the equal angles EGB, GHD (Part a) 15. Here is Playfair's Axiom: Two intersecting straight lines cannot both be parallel to a third line. 5. Apply that enunciation to the figure, and use Problem 4b to
Let the straight lines AB, CD be parallel, For, suppose that the straight line KL that passes through G is also parallel to CD. 16. If a straight line is perpendicular to one of two parallel lines, then it
is Apply that enunciation to the figure, and prove it.
Let the straight lines AB, CD be parallel,
For, angle AEF is equal to angle EFD 17. Proposition 30. Straight lines that are parallel to the same straight line are parallel Apply the enunciation to a figure, and prove it. Prove the following: 18. When a straight line meets two parallel straight lines, then the bisectors of the 19. If the straight line that bisects the exterior angle of a triangle is parallel to the 10. Triangle ABC is isosceles with AB equal to AC. Find the points Table of Contents | Introduction | Home Copyright © 2017 Lawrence Spector Questions or comments? E-mail: themathpage@yandex.com Private tutoring available. |