Algebraic Proofs

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

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

If a=b, then a*c=b*c

If a=b, then (a/c)=(b/c)

a(b+c)=ab+ac

a(b-c)=ab-ac

If a=b, then b can be substituted for a in any equation or expression

For any real number a, a=a

If a=b, then b=a

If a=b and b=c, then a=c

For any geometric figure A, A is congruent to A

If A is congruent to B, then B is congruent to A

If A is congruent to B and B is congruent to C, then A is congruent to C

If C is between A and B, then AC+CB=AB

If line segment  AB is congruent to line segment CB, then AB=CD

A geometric figure that divides a segment in to two congruent halves

A point that bisects a segment

If C is on the interior of angle ABD, then the measure of angle ABC+ the measure of angle CBD equals the measure of angle ABD

If angle A is congruent to angle B, Then the measure of angle A is equal to the measure of angle B

A geometric figure that divides an angle in to two congruent halves

What are the four types of Congruence Theorems?

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called...

These are the angles opposite each other when two lines cross. They are always equal.

Any of the four angles that do not include a region of the space between two lines intersected by a transversal.

an angle formed between parallel lines by a third line that intersects them.

It is intended as an easy way to remember that when you have two triangles and you have proved they are congruent, then each part of one triangle (side, or angle) is congruent to the corresponding part in the other.

What does this symbol mean?

What is line BD also known as?