Classify triangles by sides and by angles Find the measures of missing angles of right and equiangular triangles Find the measures of missing remote interior and exterior angles

1. Obj. 15 Triangle Angle Relationships
The student is able to (I can):
• Classify triangles by sides and by angles
• Find the measures of missing angles of right and
equiangular triangles
• Find the measures of missing remote interior and exterior
angles

2. Classifying Triangles
Triangles are classified by their side lengths and their angle
measures as follows:
• By side length
— equilateral — all sides congruent (equal)
— isosceles — two sides congruent
— scalene — no sides congruent
• By angle measure
— acute — all acute angles
— right — one right angle
— obtuse — one obtuse angle
— equiangular — all angles congruent

3. Practice
Classify each triangle by its angles and sides.
1.
3.
right
equiangular
scalene
equilateral
90°
2.
4.
110°
acute
isosceles
obtuse
isosceles

4. Triangle Angle Sum Theorem
All angles of a triangle add up to 180°.
Example: Find the measure of the missing
angle
56˚
29˚
180 — (56 + 29) = 180 — 85= 95˚

5. corollary
A theorem whose proof follows directly from
another theorem.
Right Triangle
Corollary
The acute angles of a right triangle are
complementary.
A
B
m∠A+m∠B+m∠C=180˚
m∠A + 90˚ + m∠C = 180˚
m∠A + m∠C = 90˚
C

6. Equiangular
Triangle
Corollary
The measure of each angle of an
equiangular triangle is 60˚.
Q
E
U
m∠E = m∠Q = m∠U
m∠E + m∠Q + m∠U = 180˚
m∠E + m∠E + m∠E = 180˚
3(m∠E) = 180˚
m∠E = 60˚

7. 2
exterior
interior
1
3
4
interior angle
The angle formed by two sides of a polygon
exterior angle
The angle formed by one side of a polygon
and the extension of an adjacent side
remote interior An interior angle that is not adjacent to an
angle
exterior angle

8. 2
exterior
interior
1
Exterior Angle
Theorem
3
4
The measure of an exterior angle of a
triangle is equal to the sum of its remote
interior angles.
m∠4 = m∠1 + m∠2

9. Third Angles
Theorem
If two angles of one triangle are congruent
to two angles of another triangle, then the
third pair of angles are congruent.
R
E
L
T
A
X
∠R ≅ ∠E

10. Practice
1. What is m∠1?
140°
140 = 105 + m∠1
m∠1 = 35°
2. Solve for x
5x — 60 = 2x + 3 + 15
5x — 60 = 2x + 18
3x — 60 = 18
3x = 78
x = 26
105°
15°
1
(5x‒60)°
(2x+3)°