4.1. Triangle Sum Theorem http://www.ck12.org
Isosceles: At least two sides are congruent.
Equilateral: All three sides are congruent.
Right: One right angle.
Acute: All three angles are less than 90◦.
Obtuse: One angle is greater than 90◦.
Equiangular: All three angles are congruent.
Guided Practice
- Determinem^6 1 in this triangle:
- Two interior angles of a triangle measure 50◦and 70◦. What is the third interior angle of the triangle?
- Find the value ofxand the measure of each angle.
Answers:
- 72◦+ 65 ◦+m^61 = 180 ◦.
Solve this equation and you find thatm^61 = 43 ◦.
- 50◦+ 70 ◦+x= 180 ◦.
Solve this equation and you find that the third angle is 60◦.
- All the angles add up to 180◦.
( 8 x− 1 )◦+( 3 x+ 9 )◦+( 3 x+ 4 )◦= 180 ◦
( 14 x+ 12 )◦= 180 ◦
14 x= 168
x= 12Substitute in 12 forxto find each angle.
[ 3 ( 12 )+ 9 ]◦= 45 ◦ [ 3 ( 12 )+ 4 ]◦= 40 ◦ [ 8 ( 12 )− 1 ]◦= 95 ◦
Practice
Determinem^6 1 in each triangle.
- Two interior angles of a triangle measure 32◦and 64◦. What is the third interior angle of the triangle?