Presentation on theme: "Types of Triangles Scalene A triangle with no congruent sides"— Presentation transcript:
1Types of Triangles Scalene A triangle with no congruent sides IsoscelesA triangle with 2 congruent sides and angles opposite the congruent sides are congruent.EquilateralA triangle with all sides and all angles equal.
2Right TriangleA triangle that contains a right angle.An Obtuse TriangleA triangle that contains an obtuse angle.
3Types of Lines Parallel Lines 2 lines that lie on the same plane and have no points in common or they have all points in common.Perpendicular lines2 lines that intersect to form right angles.
4Definitions and LogicEach definition can be written as a conditional statement.Example:Using the definition of a midpointIf C is the midpoint of line AB then AC=CBOrIf C is the midpoint of line AB then it divides the line into 2 congruent parts AC and BC.ACB
5Most proofs in geometry are related to logic proofs and the Law of Detachment. That is given the statement and the hypothesis to be true we can assume the conclusion is also true.Proofs can be written as:Statement/ReasonParagraph formFlow Chart Form
6Statement/Reason Form AB BCgivenABC is a right angleBy definition of perpendicular linesPerpendicular lines form right angles
7Paragraph FormSince AB BC is given then from the definition of perpendicular lines we know that ABC is a right angle because perpendicular lines form right angles.
8Flow Chart AB BC given ABC is a right angle Def. of perpendicular lines
9Postulates (Axioms)A Postulate is a statement whose truth is accepted without proof.A theorem is a statement that we can prove by deductive reasoning.
10Postulates and Theorems Reflexivea=aAny quantity is equal/congruent to itself.Symmetricif a=b then b=aAn equality may be expressed in either order
11TransitiveIf a=b and b=c then a=cQuantities equal to the same/ congruent quantities are equal to each other.SubstitutionAny quantity may be substituted for its equal/congruentIf a=b and a=c then b=c.
12AdditionIf a=b and c=d then a+c=b+d.Equal quantities added to equal quantities equal.Partitionthe whole is equal to the sum of its parts.SubtractionIf a=b and c=d then a-c=b-dEqual quantities subtracted from equal quantities are equal.
13MultiplicationIf a=b and c=d the ac=bd or If a=b and c=c then ac=bcEqual quantities multiplied by the same or equal quantities are equal. Multiplying by 2 is called the doubles postulate.DivisionQuantities divided by then same or equal quantities ( provided that you are not dividing by zero) are equal.HalvesHalves of equal quantities are equal