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