Presentation on theme: "Types of Triangles Scalene A triangle with no congruent sides Isosceles A triangle with 2 congruent sides and angles opposite the congruent sides are."— Presentation transcript:
Types of Triangles Scalene A triangle with no congruent sides Isosceles A triangle with 2 congruent sides and angles opposite the congruent sides are congruent. Equilateral A triangle with all sides and all angles equal.
Right Triangle A triangle that contains a right angle. An Obtuse Triangle A triangle that contains an obtuse angle.
Types 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 lines 2 lines that intersect to form right angles.
Definitions and Logic Each definition can be written as a conditional statement. Example: Using the definition of a midpoint If C is the midpoint of line AB then AC=CB Or If C is the midpoint of line AB then it divides the line into 2 congruent parts AC and BC. AC B
Most 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/Reason Paragraph form Flow Chart Form
Statement/Reason Form StatementReason AB BCgiven ABC is a right angleBy definition of perpendicular lines Perpendicular lines form right angles
Paragraph Form Since 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.
Flow Chart ABBC given ABC is a right angle Def. of perpendicular lines
Postulates (Axioms) A Postulate is a statement whose truth is accepted without proof. A theorem is a statement that we can prove by deductive reasoning.
Postulates and Theorems Reflexive a=a Any quantity is equal/congruent to itself. Symmetric if a=b then b=a An equality may be expressed in either order
Transitive If a=b and b=c then a=c Quantities equal to the same/ congruent quantities are equal to each other. Substitution Any quantity may be substituted for its equal/congruent If a=b and a=c then b=c.
Addition If a=b and c=d then a+c=b+d. Equal quantities added to equal quantities equal. Partition the whole is equal to the sum of its parts. Subtraction If a=b and c=d then a-c=b-d Equal quantities subtracted from equal quantities are equal.
Multiplication If a=b and c=d the ac=bd or If a=b and c=c then ac=bc Equal quantities multiplied by the same or equal quantities are equal. Multiplying by 2 is called the doubles postulate. Division Quantities divided by then same or equal quantities ( provided that you are not dividing by zero) are equal. Halves Halves of equal quantities are equal