Unit 4Triangles

Classifying Triangles by SidesScalene No sides

congruent

Isosceles 2 sides congruent

Equilateral All 3 sides congruent

Classifying Triangles by anglesAcute Triangle Has 3 acute

angles

Obtuse Triangle Has one obtuse angle

Right Triangle Has one right angle

Triangle Sum Theorem Activity1. Cut out the triangle given to you and

label the angles with numbers.2. Trace the triangle on your paper

including the labels.3. Rip off 2 of the 3 angles and arrange the

angles to discover the interior angle sum of a triangle.

4. Paste this on top of the one you traced.

Triangle Sum TheoremThe sum of the measures of the interior angles of a triangle is 180 degrees.

A

B C

180m A m B m C

Examples1. Find the measure of the angle

2. Solve for x

3. Find the measure of angle A

Exterior Angle Theorem Activity1. Cut out the triangle given to you

and label the angles with numbers.2. Trace the triangle on your paper

including the labels.3. Rip off 2 of the 3 angles and

arrange the angles to discover the exterior angle sum of a triangle.

4. Paste this on top of the one you traced.

Exterior Angle Theorem

1

A

B C

The measure of an exterior angle of a triangle is equal to the sum

of the measures of the two nonadjacent interior angles.

1m m A m B

Examples1. Find the measure of the indicated angle

2. Solve for x

3. Find the measure of the indicated angle

Isosceles Base Angle Theorem Activity1. On a piece of patty paper, use a

compass to construct a circle.2. Draw 2 segments from the center to

the edge of the circle (radii), and connect them to create triangle ABC.

3. Fold paper so that point A maps to point C.

4. What do we notice about angle A and angle C?

Base Angles TheoremIf two sides of a triangle are

congruent then the angles opposite those sides are congruent.

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

Converse of the Base Angles Theorem

A

BC

If , thenAB AC B C

If , then .B C AB AC

ExamplesSolve for x1. 2. 3.

Midsegment Discovery Activity

1. Using a straight edge, draw a triangle.  Label the vertices

A, B, and C.

2. Using a compass, construct the midpoint of and .

Label the midpoints D and E, respectively.

3. What do you notice abo

AB CB

ut the relationship between and ?DE AC

Midsegment TheoremThe segment connecting the

midpoints of 2 sides of a triangle is parallel to the third side and is half as long.

A

BC

D

E

Examples1. Find the missing length

indicated2. Solve for x

3. Find the missing length indicated.