Question

question 2/13
given: \\( \triangle a b c \\) on \\( \overline{a d} \\)
prove:
\\( m \angle a+m \angle b=m \angle b c d \\)
what statement should ethan add at step 3 \\& 5 to complete the proof?
(a) angle addition postulate; addition property
(b) triangle sum theorem; transitive property
definition of supplementary angles; transitive property
(d) linear pair theorem; addition property

Explanation:

• Step 2: The sum of the interior angles of a triangle is \(180^{\circ}\), which is the Triangle Sum Theorem.
• Step 4: Since \(m\angle A + m\angle B + m\angle BCA=180^{\circ}\) and \(m\angle BCA + m\angle BCD = 180^{\circ}\), by the Transitive Property (if \(a = b\) and \(b=c\), then \(a = c\)), we can set \(m\angle A + m\angle B + m\angle BCA=m\angle BCA + m\angle BCD\).

Answer:

B. Triangle Sum Theorem; Transitive Property