Draw the following: 1. acute triangle 2.right triangle 3.obtuse triangle 4. acute, scalene triangle 5.obtuse, isosceles triangle 6. right, scalene.

Draw the following:1. acute triangle2. right triangle3. obtuse triangle4. acute, scalene triangle5. obtuse, isosceles triangle6. right, scalene

Classify the following:

Do the following triangles exist? a right isosceles triangle a right equilateral triangle a right scalene triangle an acute scalene triangle an acute isosceles triangle an obtuse scalene triangle an obtuse isosceles triangle an obtuse equilateral triangle an acute equilateral triangle......

Angle Sum Theorem The sum of the measures of the angles of a triangle is 180.  

What is the measure of the missing angle?

ma=

What is the measure of the missing angle?

mb=

What is the measure of the missing angle?

mc=

What is the measure of the missing angle?

md=

Isosceles Triangle – at least two sides have the same length

equilateral triangle – isosceles triangle with all three sides are congruent

Parts of Isosceles Triangle:

vertex angle – between two sides

Parts of Isosceles Triangle:

base angles –

angles opposite sides

Name each part of the isosceles triangle below.

Name each part of the isosceles triangle below.

Name each part of the isosceles triangle below.

Isosceles Triangle Conj.

If a triangle is isosceles, then _____________________.

base angles are congruent

Converse of Isosceles Triangle Conjecture:

If a triangle has two congruent angles,

it is an isosceles triangle.

Equilateral Triangle

An equilateral triangle is equiangular and an equiangular triangle is equilateral.

Find the missing angle measures.

ma =

mb=

Find the missing angle measures.

mc =

md=

Find the missing angle measures.me =

mf =

mg =

Triangle Inequalities

Objectives:

1.Discover inequalities among sides and angles in triangles.

Triangle Inequalities

The sum of the lengths of the shorter two sides

of a triangle is greater than the length of the third side.

Is it possible to have a triangle with the following

side measures?

Is it possible to have a triangle with the following

side measures?

Is it possible to have a triangle with the following

side measures?

Is it possible to have a triangle with the following

side measures?

The longest side is opposite the angle with the ________ measure.greatest

The shortest side is opposite the angle with the ________ measure.smallest

Side-Angle Inequality

In a triangle, the longest side is opposite the angle with greatest measure, and the shortest side is opposite the angle with the least measure.

List the sides in order from shortest to longest.

List the angles in order from smallest to greatest measure.

If you extend one side of a triangle from the vertex, you form an exterior angle.

exterior angle

The angle adjacent to the exterior angle.

adjacent interior angle

The two angles that do not have the same vertex as the exterior angle.

remote interior angle

Triangle Exterior Angle Conjecture:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

mA=mB+mC

mA= ?

mB= ?

mC= ?