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Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent...

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Unit 4 Triangles
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Page 1: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Unit 4Triangles

Page 2: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Classifying Triangles by SidesScalene No sides

congruent

Isosceles 2 sides congruent

Equilateral All 3 sides congruent

Page 3: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Classifying Triangles by anglesAcute Triangle Has 3 acute

angles

Obtuse Triangle Has one obtuse angle

Right Triangle Has one right angle

Page 4: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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.

Page 5: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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

Page 6: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Examples1. Find the measure of the angle

2. Solve for x

3. Find the measure of angle A

Page 7: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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.

Page 8: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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

Page 9: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Examples1. Find the measure of the indicated angle

2. Solve for x

3. Find the measure of the indicated angle

Page 10: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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?

Page 11: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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

Page 12: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

ExamplesSolve for x1. 2. 3.

Page 13: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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

Page 14: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

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

Page 15: Triangles. Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent.

Examples1. Find the missing length

indicated2. Solve for x

3. Find the missing length indicated.


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