Thursday, October 19, 2006
Geometry (Class 18)
Overview
§4.1 (p.194) Triangles and Angles
§4.2 (p.202) Congruence and Triangles
Today we begin our study of triangles by reviewing how to classify triangles by length of sides or size of angles. We also learn what it means for two triangles to be congruent and how to write a congruence statement for two congruent triangles.
Key Ideas
Triangles can be classified by the length of their sides or by the size of their angles.
A triangles “full name” is created by stating its classification by angles and sides. For example, the full name of a triangle which has two equal sides and all angles less than 90˚ would be “isosceles acute triangle”.
A congruence statement for two triangles is written by matching the congruent angles of the triangles.
A congruent statement can be used to determine which angles are congruent and which sides are congruent.
Congruent triangles have reflexive, symmetric, and transitive properties.
Two triangles are congruent only if they are the same size and same shape. As a consequence we can say that two triangles are congruent if and only if each angle in one triangle is congruent to at least one angle in another triangle and each side of one triangle is congruent to at least one side of the other triangle.
Vocabulary
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Acute Triangle
Equiangular Triangle
Right Triangle
Obtuse Triangle
Hypotenuse
Leg
Adjacent side
Opposite side
Congruence Statement
Assignment
§4.1 (Txt. p.198) #10-12, 16-18, 32, 34, 37, 41, 47, 56
§4.2 (Txt. p.206) #10-16, 24
Proof for Practice 7
Group Assignment 1
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