Question

Match the reasons to the statements in the proof. Given: m 1 + m 5 = 180° m 1 + m 4 = 180° Prove: | |

1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180°

2. m∠1 + m∠5 = m∠1 + m∠4

3. m∠5 = m∠4

4. Ray YZ is parallel to Ray UV

Answer 1

The proof involves applying the properties of equality and the definition of parallel lines to deduce that Ray YZ is parallel to Ray UV based on given angle measures.

Step-by-step explanation:

The question is regarding a geometric proof that involves angles and parallel lines. Based on the given information, we can form a proof using the facts about angles and parallel lines.

1. Statement 1: m∠1 + m∠5 = 180° and m∠1 + m∠4 = 180° given.
2. Statement 2: If m∠1 + m∠5 = 180° and m∠1 + m∠4 = 180°, then m∠5 = m∠4. This is because we can use subtraction property of equality: subtract m∠1 from both sides of the equation.
3. Statement 3: If m∠5 = m∠4, then it means the angles are equal by the Transitive Property of Equality.
4. Statement 4: By definition, if alternate interior angles are equal, the lines cut by the transversal must be parallel. Therefore, Ray YZ is parallel to Ray UV.