Review: Begin at the word “We”. Every Time you move, write down the word(s) upon which you land. We in seven days! break another have will 1. Move to the.

Review:

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

you land.

We

in

seven

days!

break

another

have

will

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.

7. Move to the vertical angle.6. Move to the alternate exterior angle.

Triangles & Angle TheoremsTriangles & Angle Theorems

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

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

DF

Angle

SideVertex

The sides are DE, EF, and DF.The vertices are D, E, and F.The angles are D, E, F.

Triangles Classified by AnglesAcute Obtuse Right

60º

50º

70º

All acute anglesOne obtuse angle

One right angle

120º

43º

17º

30°

60º

Triangles Classified by Sides

Scalene Isosceles Equilateral

no sidescongruent at least two

sides congruent

all sidescongruent

Classify each triangle by its angles and by its sides.

60°

60° 60°A B

C

45°

45°

E

F G

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.

E

D F

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

Parts of Isosceles Triangles The angle formed by the congruent sides is called the vertex angle.

leg leg The congruent sides are called legs.

The side opposite the vertex is the base.

base anglebase angle

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

Base Angles Theorem (4.9)

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

If , thenACAB CB

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.

If , thenCB ACAB

Interior Angles Exterior Angles

Triangle Sum Theorem (4.1)Triangle Sum Theorem (4.1)The measures of the three interior angles

in a triangle add up to be 180º.

x°

y° z°

x + y + z = 180°

Complete the Practice Problems

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

1

2 3

m1+m2 =m3

Exterior Angle Theorem (4.3)Exterior Angle Theorem (4.3)

Complete the Practice Problems

Corollary to the Triangle Sum TheoremCorollary to the Triangle Sum Theorem

The acute angles of a right triangle arecomplementary.

x°

y°

x + y = 90º

Fill in the tableAcute Obtuse Right

Scalene

Isosceles

Equilateral