John writes the proof below to show that the sum of the angles in a triangle is equal to 1800. 5
Given: XY intersects SABC at
vertex C and is parallel
to AB
Prove: m2.1 + m_2 + m23 - 180°
Proof:
Statements
1. XYI AB,
2.m24+ m2 2 + m25 - 180°
3. 24 21:25 23
4.M24 21;m25-m23
5. m21 +22+ m23 - 180
Reasons
1.
2
3.
4.
5
Which of these reasons would John NOT need to use in his proof?
The sum of the angles on one side of a straight line is 1800
If a statement about a is true and a - b, the statement formed by replacing a with b is also true.
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.