* 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. 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• Find the measures of missing angles of right and
equiangular triangles
• Find the measures of missing remote interior and exterior
angles

2. Classifying Triangles
Recall that triangles are classified by their side lengths and
their angle measures as follows:
• By side length
— equilateral — all sides congruent (equal)
— isosceles — two or moreor moreor moreor more sides congruent— isosceles — two or moreor moreor moreor more 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.
90°
right
scalene
equiangular
equilateral
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
Right Triangle
Corollary
A theorem whose proof follows directly from
another theorem.
The acute angles of a right triangle are
complementary.
A
m∠A+m∠B+m∠C=180˚
m∠A + 90˚ + m∠C = 180˚
m∠A + m∠C = 90˚
B C
m∠A + m∠C = 90˚

6. Equiangular
Triangle
Corollary
The measure of each angle of an
equiangular triangle is 60˚.
E
Q
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. interior angle The angle formed by two sides of a polygon
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior
exterior angle
remote interior
angle
The angle formed by one side of a polygon
and the extension of an adjacent side
An interior angle that is not adjacent to an
exterior angle

8. Exterior Angle
Theorem
The measure of an exterior angle of a
triangle is equal to the sum of its remote
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior
Theorem triangle is equal to the sum of its remote
interior angles.
m∠3 + m∠4 = m∠1 + m∠2 + m∠3
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.
X
E
T
L
R
A
∠R ≅ ∠E

10. Practice
1. What is m∠1?
140°
105°
1140 = 105 + m∠1
m∠1 = 35°
2. Solve for x 15°
(2x+3)°
(5x‒60)°
5x — 60 = 2x + 3 + 15
5x — 60 = 2x + 18
3x — 60 = 18
3x = 78
x = 26