Geometrric Proofs

If $$a=b$$ , then $$\frac{a}{c}=\frac{b}{c}$$ , where $$c\ne0$$

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

If $$a\left(b+c\right)$$ , then $$a\left(b+c\right)=ab+ac$$

If $$a=b$$ , then $$a\times c=b\times c$$

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

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

If $$a=b$$ , then $$b=a$$

$$a=a$$

If $$a=b$$ , then either $$a=a$$ or $$b=b$$

Proofs

Properties

Theorems

Definitions

Postulates

Distributing a segment over a sum gives the sum of the distributed segments.

Adding two segments gives the total length of the combined segments.

Multiplying a segment by a number gives the length of the resulting segment.

Dividing a segment by a number gives the length of the resulting segment.

Subtracting one segment from another gives the length of the remaining segment.

If $$\overline{xy}=\overline{ab}$$ , then $$xy=ab$$

If $$\overline{xy}=\overline{ab}$$ and $$\overline{ab}=\overline{cd}$$ , then $$\overline{xy}=\overline{cd}$$

$$\overline{xy}=\overline{xy}$$

If $$\overline{xy}=\overline{ab}$$ , then $$\overline{ab}=\overline{xy}$$

Reflexive property

Definition of segment bisect

Definition of a midpoint

Substitution property

Adjacent Angles

Linear Pair

Complementary Angles

Supplementary Angles

Vertical Angles

$$\angle8\ \ and\ \angle7$$

$$\angle8\ and\ \angle6$$

$$\angle8\ and\ \angle5$$

$$\angle2$$

$$\angle3$$

$$\angle4$$

$$\angle5$$

$$\angle6$$

$$\angle1$$

$$\angle5$$

$$\angle3$$

$$\angle6$$

$$\angle9$$