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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)
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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
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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.
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Definition of congruent angles
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Definition of Right Angles:
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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.
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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
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Jumbled Proofs Packet
Get them in order:• Write in correct order (same or different
page)• Cut & paste in correct order on another
page
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COW Day….math XL #4 (proofs)
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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.
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Conditional Statements
• A statement with two parts: hypothesis and conclusion
IF…
THEN…
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• If you vote in the election, then ____________________. (let’s just name one option here, not all requirements)
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Converse
• Switch (transpose) the hypothesis and conclusion.
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Inverse
• Negate (____________) the hypothesis and conclusion of a conditional statement
***Use the original statement here!***
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Contrapositive
• Negate both the hypothesis and conclusion of the converse
***Inverse of the converse***
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If it is snowing, then it is cold.
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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.
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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.