Question

triangle angle theorems
proving the sum of the interior angle measures of a
triangle is 180°
given: y || z
prove: m∠5 + m∠2 + m∠6 = 180°
assemble the proof by dragging tiles to
the statements and reasons columns.

Explanation:

Step1: Use the property of parallel lines and alternate interior angles

Since \(y\parallel z\), \(\angle1\cong\angle5\) (alternate interior angles) and \(\angle3\cong\angle6\) (alternate interior angles). So \(m\angle1 = m\angle5\) and \(m\angle3=m\angle6\).

Step2: Use the linear - pair property

\(\angle1,\angle2,\angle3\) form a linear pair. By the linear - pair postulate, \(m\angle1 + m\angle2+m\angle3=180^{\circ}\)

Step3: Substitute

Substitute \(m\angle1\) with \(m\angle5\) and \(m\angle3\) with \(m\angle6\) in the equation \(m\angle1 + m\angle2+m\angle3=180^{\circ}\). We get \(m\angle5 + m\angle2+m\angle6=180^{\circ}\)

Answer:

The proof is assembled by using the alternate - interior angles theorem (for \(y\parallel z\)) to get \(m\angle1 = m\angle5\) and \(m\angle3=m\angle6\), and then using the linear - pair postulate (\(m\angle1 + m\angle2+m\angle3 = 180^{\circ}\)) and substitution to show \(m\angle5 + m\angle2+m\angle6=180^{\circ}\)