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# Given: ∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting segments.

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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

Substitution Property of Equality

Linear Pair Postulate

​m∠2+m∠3=180°​​​​ ​

m∠1=m∠3​

Jan 7, 2018

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 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
Jan 7, 2018
edited by hectictar  Jan 8, 2018