1 / 12

Section 5.3 Congruent Angles Associated with Parallel Lines

Section 5.3 Congruent Angles Associated with Parallel Lines. The Parallel Postulate. Through a point not on a line there is exactly one parallel to the given line. Euclidean Geometry treats it as a truth. Hyperbolic Geometry was discovered by trying to prove the parallel postulate.

laszlo
Download Presentation

Section 5.3 Congruent Angles Associated with Parallel Lines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 5.3 Congruent Angles Associated with Parallel Lines

  2. The Parallel Postulate • Through a point not on a line there is exactly one parallel to the given line.

  3. Euclidean Geometry treats it as a truth. • Hyperbolic Geometry was discovered by trying to prove the parallel postulate. • Spherical Geometry was discovered as another case. • We could not go to the moon without Hyperbolic Geometry.

  4. Theorem 37: If two lines ||, then each pair of alternate interior angles are congruent. 1 3 4 2 <1 and <2, <3 and <4

  5. Theorem 38: If two parallel linesare cut by a transversal then any pair of angles formed are either congruent or supplementary. 1 2 1 3 4 5 6 7 8

  6. Six Theorems about Parallel Lines • Th39: || lines => alt. ext. <s = • Th40: || lines => corr. <s = • Th41: || lines => same side int. <s supp • Th42: || lines =>same side ext.<s supp • Th43: In a plane, if a line is | to one of two || lines, it is | to the other. • Th44: Transitive Prop of || Lines If two lines are || to a third line, they are || to each other.

  7. A Crook Problem • If a||b find the measure of <1. 30 m <1 120 Draw m by || Postulate

  8. A Crook Problem • If a||b find the measure of <1. 30 30 m <1 60 120 Fill in measures of appropriate angles Then <1 is 90º

  9. If a||b find the measures of all the angles. 70 110

  10. If a||b find the measures of all the angles. 110 70 70 110 110 70 70 110

  11. Isosceles Trapezoid • A trapezoid is a four sided figure with one set of parallel sides. • An isosceles trapezoid is a trapezoid with legs congruent.

  12. Sample Problem 5 E C B • Given: Figure ABCD is Isoceles Trapezoid • Prove: <B = <C A D • … • Draw DE||AB • Draw AE • <DAE=<BEA, <BAE=<DEA • AE=AE • Triangles AEB = EAD • AB=DE • DE=DC • <DEC=<C • <B=<DEC • <B = <C • Given • Parallel Postulate • 2 pts determine a line • || lines => alt int <s = • Reflexive • ASA • CPCTC • Transitive • If legs = then base angles =. • || lines => corr. <s = • Transitive

More Related