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Q11

Expert-verified
Found in: Page 42

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Copy everything shown and write a two-column proof.Given: $m\angle 1=m\angle 2;$$m\angle 3=m\angle 4;$Prove: $m\angle SRT=m\angle STR$

See the step by step solution

## Step 1. Apply the addition property of algebra.

If $a=b$ and $c=d$, then $a+c=b+d$.

$m\angle 1+m\angle 3=m\angle 2+m\angle 4$

## Step 2. Angle addition postulate.

From the given figure, it can be observed that some of $m\angle 1$ and $m\angle 3$ gives $m\angle SRT$, that is $m\angle 2+m\angle 4=m\angle STR$.

From the given figure, it can be observed that some of $m\angle 2$ and $m\angle 4$ gives $m\angle STR$, that is $m\angle 2+m\angle 4=m\angle STR$.

## Step 3. Apply substitution property.

Substitute $m\angle SRT$ for $m\angle 1+m\angle 3$ and $m\angle STR$ for $m\angle 2+m\angle 4$ in step 1.

$\begin{array}{c}m\angle 1+m\angle 3=m\angle 2+m\angle 4\\ m\angle SRT=m\angle STR\end{array}$

## Step 4. Write a two-column proof.

Write a two-column proof with the help of the above-mentioned steps.