Please answer question 15 (2.5). Note that Theorem 5 is also attached 11. If in Problem 10 you are given the additional information that the opposite ray ofBE bisects ZABC, what values are possible for mLDBE?12. Prove the corollary to Theorem 1.13. Prove that the bisectors of a linear pair of angles are perpendicular. Establish anybetweenness relations used in the proof. (Hint: Use the Protractor Postulate to helpyou establish these betweenness relations.)14. Use the Protractor Postulate to prove that if OA, OB, OC are any three rays on oneside of a line and having the same end point, then either OA-OB-OC,ОA-ОС-ОВ, or OB-OA-OС.15. Prove Theorem 5 using the Linear Pair Axiom.16. Prove that if two angles have a side in common that passes through an interior pointof the angle formed by the other two sides, the other two sides are perpendicular iffthe given angles are complementary.17. Using Sketchpad to construct complementary angles (see figure).[1] Construct perfectly horizontal and perfectly vertical segments AB and CAand locate D any point inside ZBAC. (If you have trouble, just rotateAB 90° about A.)[2] Display angle measures x = MLDAB and y = MLCAD on the screen.(Does this sum equal 90°?)[3] Construct any segment EF elsewhere on the screen.[41 Construct an angle of measure r at E, as follows: (1) Double click on E 2.5 Angle Measure and the Protractor Postulate99THEOREM 4: Given a point A on line e, there exists a unique line m perpen-dicular to e at A.ICAL ANGLESA final useful result involves what are called vertical angles, or a vertical pair ofangles, as shown in Figure 2.37. These are two angles having the sides of one oppo-site the sides of the other, using the previous definition of opposite rays.VERTICAL PAIR2.Figure 2.37THEOREM 5: VERTICAL PAIR THEOREMVertical angles have equal measures.

Name: Please answer question 15 (2.5). Note that Theorem 5 is also attached
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Description: Please answer question 15 (2.5). Note that Theorem 5 is also attached 11. If in Problem 10 you are given the additional information that the opposite ray ofBE bisects ZABC, what values are possible for mLDBE?12. Prove the corollary to Theorem 1.13. P

Answered: Image /qna-images/answer/119dbd34-1444-49c3-ad1a-8cf00ab017c4.jpg

Answered: 5. Prove Theorem 5 using the Linear…

Math

Geometry

5. Prove Theorem 5 using the Linear Pair Axiom.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Topic Video

Question

Please answer question 15 (2.5). Note that Theorem 5 is also attached

11. If in Problem 10 you are given the additional information that the opposite ray of
BE bisects ZABC, what values are possible for mLDBE?
12. Prove the corollary to Theorem 1.
13. Prove that the bisectors of a linear pair of angles are perpendicular. Establish any
betweenness relations used in the proof. (Hint: Use the Protractor Postulate to help
you establish these betweenness relations.)
14. Use the Protractor Postulate to prove that if OA, OB, OC are any three rays on one
side of a line and having the same end point, then either OA-OB-OC,
ОA-ОС-ОВ, or OB-OA-OС.
15. Prove Theorem 5 using the Linear Pair Axiom.
16. Prove that if two angles have a side in common that passes through an interior point
of the angle formed by the other two sides, the other two sides are perpendicular iff
the given angles are complementary.
17. Using Sketchpad to construct complementary angles (see figure).
[1] Construct perfectly horizontal and perfectly vertical segments AB and CA
and locate D any point inside ZBAC. (If you have trouble, just rotate
AB 90° about A.)
[2] Display angle measures x = MLDAB and y = MLCAD on the screen.
(Does this sum equal 90°?)
[3] Construct any segment EF elsewhere on the screen.
[41 Construct an angle of measure r at E, as follows: (1) Double click on E

2.5 Angle Measure and the Protractor Postulate
99
THEOREM 4: Given a point A on line e, there exists a unique line m perpen-
dicular to e at A.
ICAL ANGLES
A final useful result involves what are called vertical angles, or a vertical pair of
angles, as shown in Figure 2.37. These are two angles having the sides of one oppo-
site the sides of the other, using the previous definition of opposite rays.
VERTICAL PAIR
2.
Figure 2.37
THEOREM 5: VERTICAL PAIR THEOREM
Vertical angles have equal measures.

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