Review:

Begin at the word “We”. Every Time you move, write down the word(s) upon which you land.

1. Move to the consecutive interior angle.

2. Move to the alternate interior angle.

3. Move to the corresponding angle.

4. Move to the alternate exterior.

5. Move to the exterior linear pair.

6. Move to the alternate exterior angle.

7. Move to the vertical angle.

We break have in will seven another days!

Triangles & Angle Theorems

Learning Target

: Students can prove geometric theorems involving lines, angles, triangles and parallelograms.

4.1 Classifying Triangles

Triangle – A figure formed when three noncollinear points are connected by segments.

E Angle The sides are DE, EF, and DF .

The vertices are D, E, and F.

The angles are  D,  E,  F.

Side Vertex F D

Triangles Classified by Angles

Acute 60º 50º Obtuse 17º 120º Right 30° 70º 43º 60º All acute angles One obtuse angle One right angle

Triangles Classified by Sides

Scalene Isosceles Equilateral no sides congruent at least two sides congruent all sides congruent

Classify each triangle by its

angles

E and by its

sides.

C 60° 45° F 45° G A 60° 60° B 

EFG

is a right isosceles triangle.



ABC

is an acute equilateral triangle

Adjacent Sides- share a vertex ex. The sides DE & EF are adjacent to  E.

Opposite Side- opposite the vertex ex. DF is opposite  E.

E D F

Parts of

Isosceles Triangles

The angle formed by the congruent sides is called the

vertex angle

.

The two angles formed by the base and one of the congruent sides are called

base angles

.

base angle leg leg The congruent sides are called

legs

.

base angle The side opposite the vertex is the

base

.

Base Angles Theorem (4.9)

If two sides of a triangle are congruent, then the angles opposite them are congruent.



B

 

C

Complete the Practice Problems

Converse of Base Angles Theorem (4.10)

If two angles of a triangle are congruent, then the sides opposite them are congruent.

AB



AC

Interior Angles Exterior Angles

Triangle Sum Theorem (4.1)

The measures of the three interior angles in a triangle add up to be 180º.

x°

x + y + z = 180°

y° z°

Complete the Practice Problems

Exterior Angle Theorem (4.3)

The measure of the exterior angle is equal to the sum of two nonadjacent interior angles

1 m



1+m



2 =m



3 2 3

Complete the Practice Problems

Corollary to the Triangle Sum Theorem The acute angles of a right triangle are

complementary

.

x + y = 90

º

x° y°

Scalene Fill in the table Acute Obtuse Right Isosceles Equilateral