1. Prove that given a line é and a point P not on e, there exists a linethrough P perpendicular to €.2. If in AABC we have ZB LC, then AB AC and AABC isisosceles.3. State and prove the Alternate Interior Angle Theorem.4. State and prove the Exterior Angle Theorem.5. Prove that in a triangle, the greater angle lies opposite the greaterside and the greater side lies opposite the greater angle.6. Prove that the angle sum of every triangle is 180° if we assumeHilbert's Euclidean parallel postulate.7. How many points and lines are there in the Fano's Geometry? Justifyyour answer.8. Draw a representation of the four-line geometry. Name all the pointsand lines.9. Draw a representation of the four-point geometry. Name all thepoints and lines.10. Draw a representation of the Young's Finite Geometry. Name all thelines and determine which lines are parallel to cach other.

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Answered: 1. Prove that given a line € and a…

Math

Algebra

1. Prove that given a line € and a point P not on e, there exists a line through P perpendicular to e.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter5: Similar Triangles

Section5.6: Segments Divided Proportionally

Problem 34E: Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the...

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Question

100%

1. Prove that given a line é and a point P not on e, there exists a line
through P perpendicular to €.
2. If in AABC we have ZB LC, then AB AC and AABC is
isosceles.
3. State and prove the Alternate Interior Angle Theorem.
4. State and prove the Exterior Angle Theorem.
5. Prove that in a triangle, the greater angle lies opposite the greater
side and the greater side lies opposite the greater angle.
6. Prove that the angle sum of every triangle is 180° if we assume
Hilbert's Euclidean parallel postulate.
7. How many points and lines are there in the Fano's Geometry? Justify
your answer.
8. Draw a representation of the four-line geometry. Name all the points
and lines.
9. Draw a representation of the four-point geometry. Name all the
points and lines.
10. Draw a representation of the Young's Finite Geometry. Name all the
lines and determine which lines are parallel to cach other.

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