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
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
– 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.
2. 4.
90°
110°

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

5. Triangle Angle SumTriangle Angle SumTriangle Angle SumTriangle Angle Sum TheoremTheoremTheoremTheorem – 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˚

6. corollarycorollarycorollarycorollary – a theorem whose proof follows directly from
another theorem.
Right TriangleRight TriangleRight TriangleRight Triangle CorollaryCorollaryCorollaryCorollary – the acute angles of a right triangle
are complementary.
A
B C
m∠A+m∠B+m∠C=180˚
m∠A + 90˚ + m∠C = 180˚
m∠A + m∠C = 90˚

7. Equiangular TriangleEquiangular TriangleEquiangular TriangleEquiangular Triangle CorollaryCorollaryCorollaryCorollary – 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˚

8. interiorinteriorinteriorinterior angleangleangleangle – the angle formed by two sides of a polygon
exteriorexteriorexteriorexterior angleangleangleangle – the angle formed by one side of a polygon
and the extension of an adjacent side
remote interiorremote interiorremote interiorremote interior angleangleangleangle – an interior angle that is not adjacent
to an exterior angle
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior

9. Exterior AngleExterior AngleExterior AngleExterior Angle TheoremTheoremTheoremTheorem – the measure of an exterior angle of
a 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
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior

10. Third AnglesThird AnglesThird AnglesThird Angles TheoremTheoremTheoremTheorem – 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

11. Practice
1. What is m∠1?
2. Solve for x
140°
105°
1
15°
(2x+3)°
(5x‒60)°

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