Question

Solve the following problems.1. Given <1 and <2 are a linear pair. 22 and 23 are a linear pair. Prove: 21€ 23.2. Given: 1 || m. Write a flowchart proof to show that Z1 Z3.

Answer 1

Recall that two angles are a linear pair if they add up to 180 degrees, therefore:

`\begin{gathered} \measuredangle1+\measuredangle2=180^(\circ), \\ \measuredangle2+\measuredangle3=180^(\circ). \end{gathered}`

Then,

`\measuredangle1+\measuredangle2=\measuredangle2+\measuredangle3.`

Subtracting ∡2 from the above equation we get:

`\begin{gathered} \measuredangle1+\measuredangle2-\measuredangle2=\measuredangle2+\measuredangle3-\measuredangle2, \\ \measuredangle1=\measuredangle3. \end{gathered}`

Therefore

`\measuredangle1\cong\measuredangle3.`