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This printable supports Common Core Mathematics Standard HSG-CO.C.9

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# Proving Alternate Interior Angles are Congruent (Grade 10)

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## Proving Alternate Interior Angles are Congruent

Add the correct reasons for the following proof.

Given the parallel lines $k$ and $m$, and transversal $t$, prove that $ang 3 ~= ang 5$.

 $" Statement "$ $" Reason "$ $1. m ang 2 + m ang 3 = 180°$ $1. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $2. m ang 5 + m ang 6 = 180°$ $2.$ $3. m ang 5 + m ang 6 = m ang 2 + m ang 3$ $3.$ $4. k " || " m$ $4.$ $5. ang 6 ~= ang 2$ $5.$ $6. m ang 6 = m ang 2$ $6.$ $7. m ang 5 + m ang 6 = m ang 6 + m ang 3$ $7. \ \ \ \$ $8. m ang 5 = m ang 3$ $8.$ $9. ang 5 ~= ang 3$ $9.$

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