Given: AABCDE ||ACProve: mLA + MLABC + mzC = 180*StatementReason1. AABC ; DE ||AC1. Given2. Supplement Postulate3. Definition of supplementary angles4. Angle Addition Postulate5. Substitution Property2. 41 and ZABE are supplementary3. m21+m 2ABE - 1804. m22 + m23 - MLABE5. m21 + m22 + m23 - 180°6. ?7. Definition of congruency8. Substitution Property6. 41 a ZA; 3 a 2C7. m21 - mLA; mL3 - m2c8. mLA + MLABC + m2C - 180°Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°.Which reason can she use to justify the statement in line 6?A.Alternate interior angles of parallel lines are congruentCorresponding angles of parallel lines are congruentExterior Angle TheoremD.Symmetric PropertyB.C.

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Given: AABC DE ||AC Prove: mLA + MLABC + m2c = 180* Statement Reason 1. AABC ; DE || AC 2. 41 and LABE are supplementary 2. Supplement Postulate 1. Given 3. me1+m LABE - 180 3. Definition of supplementary angles 4. m22+ m2a- MLABE 5. m21 + m2 + mL3 - 180° 4. Angie Addition Postulate 5. Substitution Property 7. m1 - mLA; mL3 - mLc 8. mLA + MLABC + mLC = 180° 6. 7 7. Definition of congruency 8. Substitution Property Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°. Which reason can she use to justify the statement in line 6? A. ) Alternate interior angles of parallel lines are congruent ) Corresponding angles of parallel lines are congruent В. ) Exterior Angle Theorem C. D. Symmetric Property

Given: AABC DE ||AC Prove: mLA + MLABC + m2c = 180* Statement Reason 1. AABC ; DE || AC 2. 41 and LABE are supplementary 2. Supplement Postulate 1. Given 3. me1+m LABE - 180 3. Definition of supplementary angles 4. m22+ m2a- MLABE 5. m21 + m2 + mL3 - 180° 4. Angie Addition Postulate 5. Substitution Property 7. m1 - mLA; mL3 - mLc 8. mLA + MLABC + mLC = 180° 6. 7 7. Definition of congruency 8. Substitution Property Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°. Which reason can she use to justify the statement in line 6? A. ) Alternate interior angles of parallel lines are congruent ) Corresponding angles of parallel lines are congruent В. ) Exterior Angle Theorem C. D. Symmetric Property

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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Question

Given: AABC
DE ||AC
Prove: mLA + MLABC + mzC = 180*
Statement
Reason
1. AABC ; DE ||AC
1. Given
2. Supplement Postulate
3. Definition of supplementary angles
4. Angle Addition Postulate
5. Substitution Property
2. 41 and ZABE are supplementary
3. m21+m 2ABE - 180
4. m22 + m23 - MLABE
5. m21 + m22 + m23 - 180°
6. ?
7. Definition of congruency
8. Substitution Property
6. 41 a ZA; 3 a 2C
7. m21 - mLA; mL3 - m2c
8. mLA + MLABC + m2C - 180°
Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°.
Which reason can she use to justify the statement in line 6?
A.
Alternate interior angles of parallel lines are congruent
Corresponding angles of parallel lines are congruent
Exterior Angle Theorem
D.
Symmetric Property
B.
C.

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