CK12 - Geometry

If , then.

SymmetricPropertyof Congruenceof Angles:

TransitivePropertyof Equality: If and , then

TransitivePropertyof Congruenceof Segments

If and then

TransitivePropertyof Congruenceof Angles

If , and then

.

UsingCongruencePropertiesin Equations

Whenyou solveequationsin algebrayou use propertiesofequality. You mightnot writeout the logical
justificationfor eachstep in your solution,but you knowthat thereis an equalitypropertythat justifiesthat
step.

Let’s see how we can use the propertiesofcongruenceto justifystatementsin deductivereasoning.Abbre-
viatednamesof the propertiescan be used.

Example 1

Givenpoints , and , with , and.

Are , ,and collinear?

Why do we wantthis?So that we can bring

in the numbersthat are and.

(reflexive).

Justificationis substitutionof for and

for.

; this is arithmetic.No justi-

ficationis neededas long as the arithmetic

is correct.

Morearithmetic.

Substituting for and

for.

Segmentadditionpostulate. , and

are collinear if and only if

, and arenotcollinear.

.

Example 2

Giventhat and.

Provethat is an acuteangle.