4-3 Day 1 Properties of Algebra

Algebra Properties

Identity

a+o=a

a multiplied by i=a

Communitive(order changes)

a+b=b+a

a multiplied by b = b multiplied by a.

Associative(paremthesismove)

(a+b)+c=a+(b+c)

(ab)c=a(bc)

Inverse

a+(-a)=0

a multiplied by 1 over a = 1

REFER TO 1-7 NOTES!!!

Example 1:

AM=AM (reflexive)

4-3 Day 2 Proofs

Definition of angle bisector: A ray that cuts an angle into 2 congruent angles.

Bisector Thm: If ray AY is the bisector, the measure f angle XAY = 1/2 of the measure of angle XAZ.

Midpoint Thm: Point lies directly in between 2 other points and cuts them in half.

Definition of betweeness: 3 distinct point R,S,T. S is in between R and T. If they are collinear, then RS=ST=RT.

Example 2:

Given: A is between B and C.

Prove: BA=BC-AC

Statements:

1. A is between B and C.

2. BA+AC=BC

3. BA=BC-AC

Reasons:

1. Given

2. Definition of betweeness

3. Subtration

4-3 Day 3

Thm 4-4: If a triangle is a right triangle, then the acute angles are complementary.

Thm 4-5: If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent.

Thm 4-6: All right angles are congruent.

Thm 4-7: If 2 angles are congruent and supplementary, then each angle is a right angle.

Problem 1-1

What is the answer to example 1?

Reflexive a>

Transitive a>

Glide Relection

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