Classifying Triangles by Angles

Classifying Triangles by Angles - Transcript

4 1 Classifying Triangles
Objectives
Identify and classify triangles by angles
Identify and classify triangles by sides
Vocabulary
Classify Triangles by Angles
Acute triangle
Obtuse triangle
Right triangle
Equiangular triangle
Classify Triangles by Sides
Scalene triangle
Isosceles triangle
Equilateral triangle
Coordinate Geometry
Distance Formula
ORGANIZE IT FOLDABLE 4 2 Angles of Triangles
Objectives
Apply the Angle Sum Theorem
Apply the Exterior Angle Theorem
Vocabulary
Exterior angle
Remote interior angles
Flow proof
Corollary
Theorem 4 1 Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180
Diagram
Theorem 4 2 Third Angle Theorem
If two angles of one triangle are congruent to two angles of a second triangle then the third angles of the triangles are congruent
Diagram
Theorem 4 3 Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
Diagram
Corollary 4 1
The acute angles of a right triangle are complementary
Diagram
Corollary 4 2
There can be at most one right or obtuse angle in a triangle
Diagram
ORGANIZE IT FOLDABLE

4 3 Congruent Triangles
Objectives
Name and label corresponding parts of congruent triangles
Identify congruence transformations
Vocabulary
Congruent triangles
Congruence
Transformation
Theorem 4 4 Properties of Triangle Congruence

Diagram

Diagram


Diagram
Naming Congruent Triangles
6 ways to name each pair of congruent triangles
Diagram
Identify Congruence Transformations
Slide flip or turn
Diagrams
Transformations in the Coordinate Plane
Diagrams
ORGANIZE IT FOLDABLE
4 4 Proving Congruence SSS SAS
Objectives
Use the SSS Postulate to test for triangle congruence
Use the SAS Postulate to test for triangle congruence
Vocabulary
Included Angle
Postulate 4 1 Side Side Side Congruence
If the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent SSS
Diagram
SSS in Proofs
SSS in the Coordinate Plane
Postulate 4 2 Side Angle Side Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent SAS
Diagram
SAS in Proofs
Identifying Congruent Triangles
ORGANIZE IT FOLDABLE
4 5 Proving Congruence ASA AAS
Objectives
Use the ASA Postulate to test for triangle congruence
Use the AAS Postulate to test for triangle congruence
Vocabulary
Included side
Postulate 4 3 Angle Side Angle Congruence
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent ASA
Diagram
ASA in Proofs
Theorem 4 5 Angle Angle Side Congruence
If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle then the two triangles are congruent
Diagram
AAS in Proofs
ORGANIZE IT FOLDABLE
Methods to Prove Triangle Congruence
Definition of Congruent Triangles
Diagram

SSS
Diagram

SAS
Diagram

ASA
Diagram

AAS
Diagram

Geometry Activity Congruence in Right Triangles Text pp 214 215
Right Triangle Congruence
Theorem Abbreviation Example
4 6 Leg Leg Congruence
LL
4 7 Hypotenuse Angle Congruence
HA
4 8 Leg Angle Congruence
LA
Postulate

4 4 Hypotenuse Leg Congruence
HL

Isosceles Triangles
Objectives
Use properties of isosceles triangles
Use properties of equilateral triangles
Vocabulary
Vertex angle
Base angle
Theorem 4 9 Isosceles Triangle Theorem
If two sides of a triangle are congruent then the angles opposite those sides are congruent
Diagram
Find Measures of a Missing Angle
Theorem 4 10 Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent then the sides opposite those angles are congruent
Diagram
Properties of Equilateral Triangles
Corollary 4 3
A triangle is equilateral if and only if it is equiangular
Diagram
Corollary 4 4

Diagram
ORGANIZE IT FOLDABLE
Triangles and Coordinate Proof
Objectives
Position and label triangles for use in coordinate proofs
Write coordinate proofs
Vocabulary
Coordinate proof
Placing Figures on the Coordinate Plane
Use the origin as a vertex or center of the figure
Place at least one side of a polygon on an axis
Keep the figure within the first quadrant if possible
Use coordinates that make computations as simple as possible
Example
Coordinate Proofs
ORGANIZE IT FOLDABLE
Chapter 4 Congruent Triangles
Mrs Stephanie Smith Revised September 2007
Page PAGE 1 of NUMPAGES 14