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8. Now it's your turn. Use the same logical approach to prove that the other pair of vertical angles, Lb and Ld, must also have the same measure.

8. Now it's your turn. Use the same logical approach to prove that the other pair of vertical angles, Lb and Ld, must also have the same measure.

Elementary Geometry For College Students, 7e
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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A Proof of the Vertical Angles Theorem In a proof, we first clearly state what is to be proven and what is given. Then we make our argument, justifying each statement of the argument by citing the relevant axiom or postulate. (Note that = is the symbol for congruent.) Given: Intersecting lines forming angles a, b, c, and d, with mLa + mZb3 180° and mzb+ mZc= 180° Prove: La = Lc and Lb = Ld Proof: mLa + mZb 180° and mZb + m2c = 180° are given. Therefore, mLa + mZb equal to the same thing are equal to each other. mzb + mLc, because things that are Subtracting mZb from both sides gives mLa = equals are subtracted from equals, the remainders are equal. mLc, because if Q.E.D. In the middle ages people wrote "Q.E.D." at the end of proofs. Q.E.D. stands for Quod Erat Demonstrandum, which in Latin means "it has been proven. 8. Now it's your turn. Use the same logical approach to prove that the other pair of vertical angles, Zb and Ld, must also have the same measure. In this unit you will see several new theorems. Sometimes you will need to understand someone else's proof, and sometimes you will be writing proofs of your own.
Transcribed Image Text:A Proof of the Vertical Angles Theorem In a proof, we first clearly state what is to be proven and what is given. Then we make our argument, justifying each statement of the argument by citing the relevant axiom or postulate. (Note that = is the symbol for congruent.) Given: Intersecting lines forming angles a, b, c, and d, with mLa + mZb3 180° and mzb+ mZc= 180° Prove: La = Lc and Lb = Ld Proof: mLa + mZb 180° and mZb + m2c = 180° are given. Therefore, mLa + mZb equal to the same thing are equal to each other. mzb + mLc, because things that are Subtracting mZb from both sides gives mLa = equals are subtracted from equals, the remainders are equal. mLc, because if Q.E.D. In the middle ages people wrote "Q.E.D." at the end of proofs. Q.E.D. stands for Quod Erat Demonstrandum, which in Latin means "it has been proven. 8. Now it's your turn. Use the same logical approach to prove that the other pair of vertical angles, Zb and Ld, must also have the same measure. In this unit you will see several new theorems. Sometimes you will need to understand someone else's proof, and sometimes you will be writing proofs of your own.
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