Key concepts of Properties of Real numbers and geometric quantities

Geometry A UTHS Uni 3

Addition property of equality

If a = b , then a +c = b+c

Subtraction property of equality

If a = b , then a - c = b - c

Multiplication property of equality

If a = b , then ab = bc

Division property of equality

If a = b , then a/c = b/c ( where c is not equal to 0)

Reflexive Property

• Reflexive property of congruence indicates that any geometric quantity is congruent to itself.

• For any geometric quantity a, a ≅ a

• Example : for geometric angle 45 degrees , 45 degrees ≅ 45 degrees

Symmetric property

• Indicates that if one geometry quantity is congruent to a second geometry quantity, then the second geometric quantity is also congruent to the first one.

• For any geometry quantities , a and b if a ≅ b, then b ≅ a

• Example : for line segments AB and CD, AB ≅ CD, then CD ≅ AB.

Transitive Property

• If one geometric quantity is congruent to a second geometric quantity and the second geometric quantity is congruent to a third geometric quantity, then the first and third geometric quantities are congruent.

• Example : If Jenna is the same age as Dylan and Dylan is the same age as Pedro, then Jenna is the same age as Pedro.

• Geometry example: For the line segments AB, CD, and EF, if AB ≅ CD and CD ≅ EF,then AB ≅ EF.

Substitution

• Indicates that a geometric quantity may be substituted for any equivalent geometric quantity in any geometric expression.

• For any geometric quantities where a = b, then a may be replaced by b in any geometric expression

• Example : For the line segments AB, CD, EF, where the measure of EF = 6 Units, and AB = CD + EF , then AB = CD + 6 where EF is replaced by 6.

Substitution is similar to which other property?

Transitive property.

Substitution is used when?

used when one geometric object or number is replaced.

Transitive property is used if what?

Used if the entire side of an equation is replaced by an equivalent expression.

Transitivity is what?

A special type of substitution (but substitution is NOT a type of transitivity).

Definition of congruent angles

If <A ≅ <B, then m<A = m<B. Also, if m<A = m<B, then <A ≅ <B.