14. Given: ∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting segments.
Prove: ∠1 and ∠3 are congruent.
Drag the answers into the boxes to correctly complete the proof.
Statement Reason
∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting segments. Given
∠1 and ∠2 form a linear pair. Definition of linear pair
∠2 and ∠3 form a linear pair. Definition of linear pair
m∠1+m∠2=180° Linear Pair Postulate
_____________________
m∠1+m∠2=m∠2+m∠3 ________________________
___________________________ Subtraction Property of Equality
ANSWER CHOICES
Substitution Property of Equality
Linear Pair Postulate
Addition Property of Equality
m∠2+m∠3=180°
m∠1=m∠3
Statement |
| Reason |
∠1, ∠2, ∠3, and ∠4 formed by two intersecting segments. |
| Given |
∠1 and ∠2 form a linear pair. |
| Definition of linear pair |
∠2 and ∠3 form a linear pair. |
| Definition of linear pair |
m∠1 + m∠2 = 180° |
| Linear Pair Postulate |
m∠2 + m∠3 = 180° |
| Linear Pair Postulate |
m∠1 + m∠2 = m∠2 + m∠3 |
| Substitution Property of Equality |
m∠1 = m∠3 |
| Subtraction Property of Equality |
Statement |
| Reason |
∠1, ∠2, ∠3, and ∠4 formed by two intersecting segments. |
| Given |
∠1 and ∠2 form a linear pair. |
| Definition of linear pair |
∠2 and ∠3 form a linear pair. |
| Definition of linear pair |
m∠1 + m∠2 = 180° |
| Linear Pair Postulate |
m∠2 + m∠3 = 180° |
| Linear Pair Postulate |
m∠1 + m∠2 = m∠2 + m∠3 |
| Substitution Property of Equality |
m∠1 = m∠3 |
| Subtraction Property of Equality |