O PENDINGWednesday, Apr 21, 2021MATH • ADVANCED-MATHNON EUCLIDEAN GEOMETRYWHAT IS THE FOLLOWING.1. Version of the Fifth Postulate2. Number of lines parallel to a given line,passing through a pointapart from the given line3. Sum of interior angles of a triangle on itssurface4. Model of the geometryII

Name: O PENDINGWednesday, Apr 21, 2021MATH • ADVANCED-MATHNON EUCLIDEAN GEO
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Description: O PENDINGWednesday, Apr 21, 2021MATH • ADVANCED-MATHNON EUCLIDEAN GEOMETRYWHAT IS THE FOLLOWING.1. Version of the Fifth Postulate2. Number of lines parallel to a given line,passing through a pointapart from the given line3. Sum of interior angles of

Five postulates: 1)To draw a straight line from any point to any other. 2)To produce a…

Answered: 1. Version of the Fifth Postulate

Math

Geometry

1. Version of the Fifth Postulate

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter3: Triangles

Section3.1: Congruent Triangles

Problem 8E: a. Suppose that you wish to prove that RSTSRV. Using the reason Identity, name one pair of...

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HA hypotenuse-angle is also a valid method for proving that two right triangles are congruent a Given that AD and ABDE in the right triangles shown, can HA be used to verify that ABCDEF? b Name another method SSS, SAS. etc. that can be used to verify that these triangles are congruent.
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
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
The Segment-Addition Postulate can be generalized as follows: The length of a line segment equals the sum of the length of its parts. State a general conclusion regarding AE based on the following figure.
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.
a. Suppose that you wish to prove that RSTSRV. Using the reason Identity, name one pair of corresponding parts that are congruent. b. Suppose you wish to prove that RWTSWV. Considering the figure, name one pair of corresponding angles of these triangles that must be congruent.
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._________________
Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RT