http://www.ck12.org Chapter 4. Triangles and Congruence
Given: 4 ABCwith
←→
AD||BC
Prove:m^61 +m^62 +m^63 = 180 ◦
TABLE4.1:
Statement Reason- 4 ABCabove with
←→
AD||BC Given2.^61 ∼=^64 ,^62 ∼=^65 Alternate Interior Angles Theorem
3.m^61 =m^64 ,m^62 =m^65 ∼=angles have = measures
4.m^64 +m^6 CAD= 180 ◦ Linear Pair Postulate
5.m^63 +m^65 =m^6 CAD Angle Addition Postulate
6.m^64 +m^63 +m^65 = 180 ◦ Substitution PoE
7.m^61 +m^63 +m^62 = 180 ◦ Substitution PoE
There are two theorems that we can prove as a result of the Triangle Sum Theorem and our knowledge of triangles.
Theorem #1:Each angle in an equiangular triangle measures 60◦.
Theorem #2:The acute angles in a right triangle are always complementary.
Example A
What is them^6 T?
From the Triangle Sum Theorem, we know that the three angles add up to 180◦. Set up an equation to solve for^6 T.
m^6 M+m^6 A+m^6 T= 180 ◦
82 ◦+ 27 ◦+m^6 T= 180 ◦
109 ◦+m^6 T= 180 ◦
m^6 T= 71 ◦