Download Section 3-4 Angles of Triangles

Section 3-4 Angles of
Triangles
What is a triangle?
Triangles
 Definition
A
figure where three segments join
at three points
 Parts
 Vertex
 Sides
Classifying or Describing
Triangles
 Sometimes
by the number of
congruent SIDES
 Sometimes
ANGLES
by the its
Classifying by Sides
 Scalene
triangle
 No congruent sides
 Isosceles triangle
 At least two congruent sides
 Equilateral triangle
 All sides congruent
Classifying by Angles

Acute

Obtuse

Right

Equiangular
 Three
acute
angles
 One obtuse
angle
 One right
angle
 All congruent
angles
Side Note

Often diagrams needed for proofs are
lacking elements.

If this is the case an AUXILIARY LINE
(or ray or segment) can be drawn to help
with the proof.

AUXILIARY LINES are denoted using a
dotted/dashed line.
Theorem 3-11
The sum of the measures of
the angles of a triangle is 180.
Prove using the diagram on the
board.
Practice
Find the missing angle then
state whether the triangles
are acute, obtuse or right





1.
2.
3.
4.
5.
55, 43
47,43
80,75
33, 33
24, 66





1.
2.
3.
4.
5.
Acute
Right
Acute
Obtuse
Right
Review: What can be used as
reasons in a proof?
 Properties/Properties
 Given
 Theorems
we already proved
 And …
A Corollary
- a statement easily proved after
a theorem is given
Now that we have theorem 3-11
What can be said about
equiangular triangles?
Corollary 2
Each angle of an equiangular
triangle is 60°.
Draw me a equiangular triangle.
Using theorem 3-11
Can a triangle have two angles
greater than or equal to 90°?
Draw me a triangle with two obtuse angles?
Can it be done? What about with two right
anlges?
Corollary 3
In a triangle, there can be at
most one right or obtuse angle.
Using theorem 3-11
In a right triangle what can be
said about the two other angles?
Draw me a right triangle and make a
conclusion about the other two angles.
Corollary 4
The acute angles of a right
triangle are complementary.
Using theorem 3-11
If triangle 1 has angles 30, 70
and y and triangle 2 has
angles x, 70 and 30 then what
do we know about x and y?
Corollary 1
If two angles of one triangle are
congruent to two angles of
another triangle, then the third
angles are congruent.
Finding the missing angle
measurements of triangles.
Using the transparency find
the measure of angle A.
Theorem 3-12
The measure of an exterior
angle of a triangle equals the
sum of the measures of the
two remote interior angles.
Now let’s look at the CE on
p.96
Homework:Written
exercises
pg 97 #1-16