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

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Presentation transcript:

Triangles

Classifying Triangles by Sides ScaleneNo sides congruent Isosceles2 sides congruent EquilateralAll 3 sides congruent

Classifying Triangles by angles Acute TriangleHas 3 acute angles Obtuse TriangleHas one obtuse angle Right TriangleHas one right angle

Triangle Sum Theorem Activity 1. 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 Theorem The sum of the measures of the interior angles of a triangle is 180 degrees.

Examples 1.Find the measure of the angle 2. Solve for x 3. Find the measure of angle A

Exterior Angle Theorem Activity 1. 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

Examples 1. Find the measure of the indicated angle 2. Solve for x 3. Find the measure of the indicated angle

Isosceles Base Angle Theorem Activity 1. 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 Theorem If 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 B C

Examples Solve for x

Midsegment Discovery Activity

Midsegment Theorem A B C D E

Examples 1.Find the missing length indicated2. Solve for x 3. Find the missing length indicated.