Download Unit 4 - My CCSD

Triangles
Classifying Triangles by Sides
Scalene
No sides
congruent
Isosceles
2 sides congruent
Equilateral
All 3 sides
congruent
Classifying Triangles by angles
Acute Triangle
Has 3 acute angles
Obtuse Triangle
Has one obtuse
angle
Right Triangle
Has 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.
A
B
mA  mB  mC  180
C
Examples
1. Find the measure of the angle
3. Find the measure of angle A
2. Solve for x
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
The measure of an exterior angle of a triangle is equal to the sum
of the measures of the two nonadjacent interior angles.
m1  mA  mB
1
Examples
1. Find the measure of the indicated angle
3. Find the measure of the indicated angle
2. Solve for x
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.
A
If AB  AC , then B  C
B
Converse of the Base Angles Theorem
 If two angles of a triangle are congruent,
then the sides opposite those angles are
congruent.
If B  C , then AB  AC.
C
Examples
Solve for x
1.
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 AB and CB.
Label the midpoints D and E, respectively.
3. What do you notice about the relationship between DE and AC ?
Midsegment Theorem
 The segment connecting the midpoints of 2
sides of a triangle is parallel to the third side
A
and is half as long.
1
𝐷𝐸 ∥ 𝐴𝐵 𝑎𝑛𝑑 𝐷𝐸 = 𝐴𝐵
2
B
D
C
E
Examples
1. Find the missing length indicated
3. Find the missing length indicated.
2. Solve for x