Questions: Fill in the blanks to complete the geometric proof. Given: angle 1 and angle 2 are supplementary angle 2 and angle 3 are supplementary Proof: angle 1 congruent to angle 3 Statements Reasons angle 1 and angle 2 Supp angle 2 and angle 3 Supp Given Definition of supplementary angles m angle 1 + m angle 2 = m angle 2 + m angle 3 m angle 1 = Subtraction Prop of Equality angle 1 congruent to angle 3

Solution Steps

To complete the geometric proof, we need to use the properties of supplementary angles and the transitive property of equality. Since angles 1 and 2 are supplementary, their measures add up to 180 degrees. Similarly, angles 2 and 3 are supplementary, so their measures also add up to 180 degrees. By setting these two equations equal to each other and using the subtraction property of equality, we can show that the measure of angle 1 is equal to the measure of angle 3, thus proving that angle 1 is congruent to angle 3.

To complete the geometric proof, we need to fill in the blanks with appropriate statements and reasons. Let's go through the proof step by step.

• Statement: \(\angle 1\) and \(\angle 2\) are supplementary.
• Statement: \(\angle 2\) and \(\angle 3\) are supplementary.
• Reason: Given.

• Statement: \(m\angle 1 + m\angle 2 = 180^\circ\) and \(m\angle 2 + m\angle 3 = 180^\circ\).
• Reason: Definition of supplementary angles.

• Statement: \(m\angle 1 + m\angle 2 = m\angle 2 + m\angle 3\).
• Reason: Both expressions equal \(180^\circ\).

• Statement: Subtract \(m\angle 2\) from both sides: \[ m\angle 1 = m\angle 3 \]
• Reason: Subtraction Property of Equality.

• Statement: \(\angle 1 \cong \angle 3\).
• Reason: If two angles have the same measure, they are congruent.

Final Answer