Question

What is the missing reason in steps 7 and 8 of the proof?



Given: ∆ABC with AB = c, BC = a, AC = b
Prove: = =

Statement Reason
1. Draw a line through B that is perpendicular to and label the point of intersection with as D. construction
2. In ∆ABD, BD = c sin A definition of sine in right triangle
3. In ∆CBD, BD = a sin C definition of sine in right triangle
4. c sin A = a sin C Substitution Property of Equality
5. = dividing throughout by sin A
sin C
6. Draw a line through A that is perpendicular to and label the point of intersection with as E. construction
7. In ∆BA

Answer 1

7. In ∆BAE, AE = c sin B
8. In ∆CAE, AE = b sin C
9. c sin B = b sin C Substitution Property of Equality
10. = dividing throughout by sin B
sin C
11. = = Transitive Property of Equality

definition of cosine in right triangle

definition of sine in right triangle

definition of tangent in right triangle

Corresponding sides of congruent triangles are equal.

definition of equilateral triangle

Answer 2

@TheSmartOne

Answer 3

a very long question just to say ...definition of sin in right triangle for 7 and 8