3
QuizMultiple Choice

Law of Cosines

Question 3 • OH-Geometry B

Consider the proof.Given: In △ABC, BD ⊥ ACProve: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason1.In △ABC, BD ⊥ AC1.given2.In △ADB, c2 = x2 + h22.Pythagorean thm. 3.In △BDC, a2 = (b – x)2 + h23.Pythagorean thm. 4.a2 = b2 – 2bx + x2 + h24.prop. of multiplication5.a2 = b2 – 2bx + c25.substitution6.In △ADB, cos(A) = 6.def. cosine7.ccos(A) = x7.mult. prop. of equality8.a2 = b2 – 2bccos(A) + c28.?9.a2 = b2 + c2 – 2bccos(A)9.commutative propertyWhat is the missing reason in Step 8?

Question illustration
Answer
A
Pythagorean theorem
B
definition of cosine
C
substitution
D
properties of multiplication