Download By its Sides By its Angles

5.2 Objective: Prove theorems about triangles
Classify each triangle
By its Sides
By its Angles
Equilateral
3  sides
Equiangular
3  angles
Acute
Isosceles
2  sides
Scalene
3 acute angles
Right
No  sides
1 right angle
Obtuse
1 obtuse angle
Parts of triangles
A, B, & C are the vertices
AB, BC & CA are the sides
BC is opposite of angle A
𝐴𝐵 & AC are adjacent angle A
B
A
C
Parts of a right triangles
A, B, & C are the vertices
AC, BC are the legs
BA is the hypotenuse
Parts of an isosceles triangles
A, B, & C are the vertices
AC, AB are the legs
CB is the base
Angles B & C are the base angles
Angle A is the vertex angle
A
B
C
A
C
B
Triangle Sum Theorem
m A + m B + m C = 180°
The sum of the measures of the
3 angles of a triangle is 180°
A
C
B
Exterior Angles Theorem
The exterior angles of a triangle sum to 360°. In
fact, the exterior angles of any convex polygon sum
to 360°
A
C
B
Exterior Angle Theorem
m 1 = m 2 + m 3
The measure of an exterior angle is equal to the
sum of the measures of the two nonadjacent
interior angles.
2
1
3
Example: Find the x then find the measure of the
exterior angle.
x°
72°
One angle of a triangle is 3 times larger than the first angle. The
second angle is ½ the first angle. Find the measures of all three
angles?
Isosceles Triangle Sum Theorem
If a triangle is an isosceles triangle, then its base
angles are congruent.
mB=mC
and
BC
A
B
C
Example 3: Three angles of a triangle are in an
extended ratio of 1:3:5. Write an equation to find
the measure of each angle, then find the measure of
each angle.
Midsegment Theorem
If D is a midpoint of 𝐴𝐶 and E is a midpoint of 𝐴𝐵
then 𝐷𝐸 is a midsegment of ∆ABC and midsegment
1
𝐷𝐸 = 𝐶𝐵.
2
Example: Find the length of 𝐷𝐸 if 𝐶𝐵 = 8.
Triangle Proportionality Theorem
If 𝐷𝐸 ∥ 𝐶𝐵, then
𝐴𝐷
𝐷𝐶
=
𝐴𝐸
𝐸𝐵
Example:
4
x
16
8