Download Triangles and Angles

Objective: 4.1 Classifying Triangles
4.2 – Angles in Triangles
Warm Up - State the number of
sides in each geometric figure.
1. Trapezoid
2. Equilateral triangle
3. Rhombus
4. Parallelogram
5. Scalene triangle
Objective: 4.1 Triangles and Angles
Triangles
• Triangle-figure formed by 3
segments joining 3
noncollinear pts.
• Triangles are named by
these three pts (ΔQRS)
Q
R
S
By Angle Measures
Triangle Classification
Acute Triangle
Three acute angles
By Angle Measures
Triangle Classification
Equiangular Triangle
Three congruent acute angles
**This is a special case of “acute triangle”
By Angle Measures
Triangle Classification
Right Triangle
One right angle
By Angle Measures
Triangle Classification
Obtuse Triangle
One obtuse angle
By Side Lengths
Triangle Classification
Equilateral Triangle
Three congruent sides
By Side Lengths
Triangle Classification
Isosceles Triangle
At least two congruent sides
By Side Lengths
Triangle Classification
Scalene Triangle
No congruent sides
• Each of the three
pts are vertices
• Adjacent sides2 sides sharing a
common vertex
• Third side is
opposite the given
vertex.
B
A
C
Parts of a Right Triangle
Leg
Leg
Parts of an Isosceles Triangle
Leg
__
___
Base
Leg
Ex. 1
It is possible to draw a right isosceles
triangle?
Is it possible to draw an isosceles
equilateral triangle?
Is it possible to draw an obtuse scalene
triangle?
Interior Angles
A
)))
B
C
Exterior Angles
(formed by extending the sides)
(
E
D
F
Thm 4.1 - Triangle Angle Sum Theorem
• The sum of the measures of
the interior angles of a
triangle is 180o.
A
• mA + mB+ mC=180o
B
C
Thm 4.2 - Exterior Angles Theorem
• The measure of an
exterior angle of a
triangle is equal to the
sum of the measures of
the 2 nonadjacent
interior angles.
• m1 = mA+ mB
B
Remote Interior Angles
A
1
C
Ex: Find the value for x
• Use the Exterior Angle
Thm
A
65
B
x
(2x + 10)
C
Third Angles Theorem
D
A
E
F
B
C
If two angles of ABC are congruent two angles
of DEF, then the third angles must be
congruent
Corollaries to Triangle Sum Thm
(Corollary- a statement easily
A
proved using a thm.)
• The acute angles of a right
triangle are
complementary.
• There can be at most one
right or obtuse angle in a
triangle.
B
A is comp. to C
B is the only right
angle
C
Ex 3: Find the measure of each acute angle.
* Use the corollary to the
triangle sum thm
• Let x = m < A and
m < B = 2x
B
2x
x
C
A