Property of Equality
Name the Property of Equality that states: For any segment AB, AB=AB.
Reflexive Property of Equality
Rewrite in the conditional form. All birds have feathers.
If it is a bird, then it has feathers.
B is the midpoint of AC.
How do we know AB is congruent to BC?
Definition of Midpoint
If the product of two numbers is positive, then the two numbers must also be positive.
For example: -5 x -3 =15
(Counterexample should have two negative numbers multiplying to be a positive)
Write the next 3 numbers in the series... 3,7,11,15,___,___,___
19,23,27
Name the Property of equality used. If a-5=10, then a=15
Addition Property of Equality
Write the converse. If you studied, then you passed.
If you passed, then you studied.
<ABC and <CBD are adjacent.
How do we know "<ABC + <CBD = <ABD"?
Angle Addition Postulate
The sum of one positive and one negative is always a positive.
For example: -7 + 5 = -2
(Counterexample should have the sum of one positive and one negative equaling a negative number)
If angle 1 and angle 2 form a vertical pair and the measure of angle 1 = 149*, what is the measure of angle 2?
149*
Name the POE that states: For any segments AB, CD, and EF, if AB=CD and CD=EF, then AB=EF
Transitive Property of Equality
Write the Inverse if the conditional statement. If I am hungry, then I will eat.
If I am not hungry, then I will not eat.
<A and <B are vertical angles.
How do we know <A is congruent to <B.
Vertical Angles Theorem
All quadrilaterals are equilateral.
Ex: rectangle
(any four sided figure where the sides are not all congruent)
If angle 1 and angle 2 form a linear pair and angle 1 = 43*, what is the measure of angle 2?
137*
Name the Property of Equality used. If 5x=30, then x=6.
Division Property of Equality
Write the contrapositive. If I am tired, then I take a nap.
If I do not take a nap, then I am not tired.
<A and <B are supplementary.
How do we know "<A + <B = 180"?
Definition of Suppplementary
All shapes are polygons
Ex: circle
(any figure with rounded sides)
If angle A and angle B are vertical angles and angle A=5x+3 and angle B=43*. Find the value of x.
8
Name the Property of Equality used. If AB+BC=AC and AB=7, then 7+BC=AC.
Substitution Property of Equality
Use the Law of Syllogism to write a new conditional statement that follows from the pair of statements. If you get a job, then you can buy a car. If you buy a car, then you can drive to school.
If you get a job, then you can drive to school.
We figure out that AB + BC = AC and AB + BC = BD.
How do we know that AC = BD?
Transitive Property of Equality
All pentagons are convex.
If angle 1 and angle 2 form a linear pair and the measure of angle 1 = 3y+11 and the measure of angle 2 = 10y, what is the value of y?
13