CK12 - Geometry

• Understandproofsof the theoremsaboutspecialpairsof angles.


• Applythe theoremsin problemsolving.

Introduction

So far mostof the thingswe haveprovenhavebeenfairlystraightforward.Now we havethe toolsto prove
somemorein-depththeoremsthat may not be so obvious.We’ll start with theoremsaboutspecialpairsof
angles.Theyare:

• right angles


• supplementaryangles


• complementaryangles


• verticalangles

RightAngleTheorem

If two anglesare right angles,then the anglesare congruent.

Given: and are right angles.

Prove:

Statement Reason

1. and are right angles. Given


2. , Definitionof right angle


3. Substitution


4. Definitionof congruentangles

Supplementsof the SameAngleTheorem

If two anglesare both supplementaryto the sameangle(or congruentangles)then the anglesare congruent.

Comments:As an example,we knowthat if is supplementaryto a angle,then.

If is also supplementaryto a angle,then too, and

Given: and are supplementaryangles. and are supplementaryangles.

Prove:

Statement Reason

1. and are supplementaryangles. Given


2. and are supplementaryangles. Given
   3. ,Definitionof supplementaryangles


3. Substitution


4. AdditionPropertyof Equality