Question

complete the two - column proof by filling in the blanks. given: △acd is isosceles with base cd, ∠1≅∠2, bd≅ce. prove: △abc≅△aed. complete the proof. statements reasons 1. m∠1 + m∠3 = 180°, m∠2 + m∠4 = 180° 1. definition of ≅ angles 2. m∠1 + m∠3 = m∠2 + m∠4 2. substitution property of equality 3. ∠1≅∠2 3. given 4. m∠1 = m∠2 4. reflexive property of equality 5. m∠1 + m∠3 = m∠1 + m∠4 5. transitive property of equality, (2, 4) 6. m∠3 = m∠4 6. subtraction property of equality, (5) 7. ∠3≅∠4 7. linear pair theorem, (6) 8. △acd is isosceles with base cd 8. given 9. ac≅ad 9. definition of ≅ segments, (8) 10. bd≅ce 10. symmetric property of ≅ 11. bd = ce 11. symmetric property of equality, (10) 12. bc + cd = cd + de 12. segment addition postulate, (11) 13. bc = de 13. subtraction property of equality, (12) 14. bc≅de 14. substitution property of ≅, (13) 15. △abc≅△aed 15. sas postulate, (7, 9, 14)

Explanation:

Answer:

1. Definition of a linear - pair of angles
2. Definition of congruent angles
3. Definition of congruent angles
4. Definition of an isosceles triangle
5. Given
6. SAS (Side - Angle - Side) congruence criterion for triangles

Discipline: Mathematics
Subfield: Geometry