2-6+Angle+Proofs

2-6 Proofs with Angles

=** 2-6: Proving Statements about Angle Relationships Using Two Column Proofs **=

In this lesson you will learn how to write a proof with angles. can follow along by looking in section 2-6 in your textbook. It thoroughly explains the section if you need another recourse. If you do not, then continue reading and learn about angle.


 * // Websites: //**

http://www.mrperezonlinemathtutor.com/G/1_3_Proofs_Segments_Angle_Relationships.html

 * // Vocabulary and Theorems: //**


 * Properties of Angle Congruence**

Reflexive- for any angle A, <A ≅ <A

Symmetric- If <A≅ <B, then <B ≅ <A

Transitive- If <A ≅ <B, and <B ≅ <C then <A ≅ <C


 * Congruent Supplements Theorem**

If two angles are supplementary to the same angle, then they are congruent

If m<1 + m<2 = 180° and m<2 + m<3 = 180°, then <1 ≅ <3


 * Congruent Complements Theorem**

If two angles are complementary to the same angle, then they are congruent.

If m<4 + m<5 = 90° and m<5 + m<6 = 90°, then <4 ≅ <6


 * // Example Problems: //**

1) Use the Right Angle Congruence theorem that all right angles are congruent.


 * Given :** <1 and <2 are right angles
 * Prove :** <1≅ <2


 * Statements || Reasons ||
 * <1 and <2 are right angles || Given ||
 * m<1 = 90°, m<2 = 90° || Definition of a right angle ||
 * m<1 = m<2 || Transitive Property ||
 * <1 ≅ <2 || Definition of Congruency ||

2) Make a two-column proof for the following situation.

Prove the transitive property


 * Given :** <A ≅ <B, <B ≅ <C
 * Prove :** <A ≅ <C

<B ≅ <C || Given ||
 * Statements || Reasons ||
 * <A ≅ <B
 * m<A = m<B || Definition of Congruency ||
 * m<B = m<C || Definition of Congruency ||
 * m<A = m<C || Transitive Property ||
 * <A ≅ <C || Definition of Congruency ||

3) Make a two-column proof for the following situation.


 * Given :** <1 and <2 are right angles
 * Prove :** <1≅ <2




 * Statements || Reasons ||
 * <1 and <2 are right angles || Given ||
 * m<1 = 90°, m<2 = 90° || Definition of congruency ||
 * m<1 = m<2 || Transitive Property ||
 * <1 ≅ <2 || Definition of Congruency ||

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 * // Your Turn! //**


 * Note: not all rows need to be used

1) Fill in the two-column proof for the following situation.


 * Given :** <1 and <2 are supplements, <3 and <4 are supplements, <1 ≅ <4
 * Prove :** <2 ≅ <3

m<3 + m<4 = 180° ||  ||
 * Statements || Reasons ||
 * || Given ||
 * m<1 + m<2 = 180°
 * || Transitive Property ||
 * m<1 = m<4 ||  ||
 * || Substitution ||
 * m<2 = m<3 ||  ||
 * || Definition of Congruency ||

2) Fill in the two-column proof for the following situation.


 * Given :** <5 and <6 are a linear pair, <6 and <7 are a linear pair
 * Prove :** <5 ≅ <7
 * Statements || Reasons ||

3) Fill in the two-column proof for the following situation.


 * Given :** <1 and <2 are complements, <3 and <4 are complements, <2 ≅ <4
 * Prove :** <1 ≅ <3


 * Statements || Reasons ||

4) Fill in the two-column proof for the following situation.


 * Given :** <QVW and <RWV are supplementary
 * Prove :** <QVP ≅ <RWV




 * Statements || Reasons ||