Welcome back…hope you had a wonderful break!

Bellringer…Monday (Everyone: new sheet of GRAPH paper, label with name, date)

Graph the line segment & find its length:

T (4, -3) H (-5, 2)

Properties of Equality

• Addition Property: If a=b, then a + c= _____.• Subtraction Property: If a=b, then a – c= _____.• Multiplication Property: If a = b, then a*c = ____.• Division Property: If If a = b and c ≠ 0, then

Properties of Equality ( ) or Congruence ( )

Reflexive Property of __________: a = a… <A <A

Symmetric Property of _________: If a = b, then b = a.

If < A < B, then <B <A.Transitive Property of __________:

If a = b and b = c, then _______.If < A < B and < B < C, then < A < C.

Definition of congruent angles

Definition of Right Angles:

Prove it!

Statements: Reasons:

1. <A is a right angle. 1.

2. <B is a right angle. 2.

3. m<A = 90° 3.

4. 4.Definition of right angle.

5. 5.Substitution.

6. <A < B 6. Definition of congruent angles.

If <A and <B are supplementary and < B and < C are congruent. Prove that m<A + m<C=180*.

Statements Reasons1. <A & <B are supplementary 1. Given

2. <B & <C are congruent 2. Given

3. m<A + m<B =180* 3. Def. of supplementary

angles

4. m<B = m<C 4. Def. of congruent

angles

5. m<A + m<C = 180* 5. Substitution

Jumbled Proofs Packet

Get them in order:• Write in correct order (same or different

page)• Cut & paste in correct order on another

page

COW Day….math XL #4 (proofs)

Bellringer…Tuesday

COPY the following and DRAW a picture showing the points are collinear:

Given: H, I, J, and K are collinear points

HJ = IK

Prove: HI = JK and that the same segments are congruent.

Conditional Statements

• A statement with two parts: hypothesis and conclusion

IF…

THEN…

• If you vote in the election, then ____________________. (let’s just name one option here, not all requirements)

Converse

• Switch (transpose) the hypothesis and conclusion.

Inverse

• Negate (____________) the hypothesis and conclusion of a conditional statement

***Use the original statement here!***

Contrapositive

• Negate both the hypothesis and conclusion of the converse

***Inverse of the converse***

If it is snowing, then it is cold.

Which is true???

Converse: If it is cold, then it is snowing.

Inverse: If it is not snowing, then it is not cold.

Contrapositive: If it is not cold, then it is not snowing.

Write the three other statements for the statements below. Then tell whether each statement is true (T) or false (F).

1. If a polygon is a triangle, then the sum of the measures of its interior angles is 180*.

2. If you drive a car, then you are at least 16 years old.

3. If two angles are vertical angles, then they are congruent.