Question

instruction
active
proving the sum of the interior angle measures of a
triangle is 180°
given: y || z
prove: m∠5 + m∠2 + m∠6 = 180°

Explanation:

Step1: Use alternate - interior angles

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

Step2: Use alternate - interior angles

Also, since \(y\parallel z\), \(\angle3\cong\angle6\) (alternate - interior angles). So \(m\angle3=m\angle6\).

Step3: Use linear - pair property

\(\angle1,\angle2,\angle3\) form a linear pair. So \(m\angle1 + m\angle2+m\angle3=180^{\circ}\) (linear - pair postulate: the sum of angles in a linear pair is \(180^{\circ}\)).

Step4: 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 completed as shown in the steps above.