Consider the proof.
given: in △abc, bd ⊥ ac
prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(a)
statement
reason
1. in △abc, bd ⊥ ac 1. given
2. in △adb, c2 = x2 + h2 2. pythagorean thm.
3. in △bdc, a2 = (b – x)2 + h2 3. pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. in △adb, cos(a) = 6. def. cosine
7. ccos(a) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(a) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(a) 9. commutative property
what is the missing reason in step 8?
a. pythagorean theorem
b. definition of cosine
c. substitution
d. properties of multiplication