KM bisects ZJKL Given: Prove: MZMKL = MLJKL Statements 1 given Def of an angle bisector 3. angle addition substitution | 5. sim Plify |adivision property 1. KM bisects ZJKL Reasons 2. MZJKM = MZMKL %3D 2. 3. MZJKM+ MZMKL = MZJKL 4. MZMKL + MZMKL = MZJKL %3D 4. 5. 2MZMKL = MZJKL %3D 6. MZMKL : %3D MZJKL 6. 12. Given: BD I BC; LABD = ZDBE Prove: ZABD and ZEBC are complementary B. Statements Reasons 1. BD 1 BC 1. 2. ZDBC is a right angle 2. 3. m/DBC = 90° 3. 4. MZDBE + MZEBC = mZDBC 4. %3D 5. MZDBE + MZEBC = 90° 5. 6. ZABD = ZDBE 6. 7. MLABD = MZDBE 7. %3D 8. MLABD + MZEBC = 90° 8. %3D 9. ZABD and ZEBC are complementary 9. 13. Given: Z1 and 24 form a linear pair;
KM bisects ZJKL Given: Prove: MZMKL = MLJKL Statements 1 given Def of an angle bisector 3. angle addition substitution | 5. sim Plify |adivision property 1. KM bisects ZJKL Reasons 2. MZJKM = MZMKL %3D 2. 3. MZJKM+ MZMKL = MZJKL 4. MZMKL + MZMKL = MZJKL %3D 4. 5. 2MZMKL = MZJKL %3D 6. MZMKL : %3D MZJKL 6. 12. Given: BD I BC; LABD = ZDBE Prove: ZABD and ZEBC are complementary B. Statements Reasons 1. BD 1 BC 1. 2. ZDBC is a right angle 2. 3. m/DBC = 90° 3. 4. MZDBE + MZEBC = mZDBC 4. %3D 5. MZDBE + MZEBC = 90° 5. 6. ZABD = ZDBE 6. 7. MLABD = MZDBE 7. %3D 8. MLABD + MZEBC = 90° 8. %3D 9. ZABD and ZEBC are complementary 9. 13. Given: Z1 and 24 form a linear pair;
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:Given: KM bisects ZJKI.
1
Prove: M2MKL =-M2JKL
Statements
1. KM bisects ZJKL
Reasons
1. diven
Def of an angle bisector
3. angle addition
substitution
5.
2. MZJKM = MZMKL
2.
3. MZJKM + M2MKL = MZJKL
4. M2MKL + MZMKL = M2JKL
4.
5. 2MZMKL = MZJKL
simPlify
|a.division property
6. MZMKL =
SMLJKL
12. Given:
BD I BC; ZABD = ZDBE
Prove: ZABD and ZEBC are complementary
Statements
Reasons
1. BD I BC
1.
2. ZDBC is a right angle
2.
3. m/DBC = 90°
3.
4. MZDBE + MZEBC = M2DBC
4.
5. MZDBE + MZEBC = 90°
5.
6. ZABD = ZDBE
6.
7. MLABD = MZDBE
7.
8. MLABD + MZEBC = 90°
8.
9. ZABD and ZEBC are complementary
9.
13. Given: Z1 and 24 form a linear pair;
21 and 2 are supplementary
Prove: 23 4
Statements
Reasons
1. 41 and 24 form a linear pair
1.
LiandL4
1and 2
2.
2. Supplement Theorem
3.
3. Given
4.
4. Congruent Supplements Theorem
5. vertical Ang lesth
5. 22 23
6. <3
6. Transitive Property
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