Download Chapter 4.1 Notes: Apply Triangle Sum Properties

Topic 3: Congruent Triangles
1.5: Triangles
Classifying Triangles by Angles
Classifying Triangles by Sides
An equilateral triangle is also equiangular
4.1 :Triangle Sum Theorem
(Interior angle sum)
4.2 Properties of Isosceles Triangles
Triangle Sum Investigation
Step 1
Step 2
Step 3
Write the letters a, b, and c
in the interiors of the three
angles
a + b + c = 180°
Triangle Sum Theorem
The sum of the measures of the
interior angles in every triangle is
180o.
1
3
2
m<1 + m<2 + m<3 = 180°
The sum of all the angles
equals 180º degrees.
Equilateral / Equiangular Triangle
60º
60º
60º
What can we find out?
The ladder is leaning
on the ground at a
75º angle. At what
angle is the top of
the ladder touching
the building?
180 = 75 + 90 + x
180 = 165 + x
X=
75
Corollary of the Triangle Sum Theorem
corollary
A
is a statement that readily
follows from a theorem.
The acute angles of a right triangle are
complementary.
m∠A + m∠B = 90o
Find the missing angles.
2x + (x – 6) = 90˚
3x – 6 = 90
3x = 96
X= 32
2x = 2(32) = 64 64˚
(x – 6) = 32 – 6 = 2626˚
The angles measure 64° and 26° respectively.
4.2: Isosceles Triangles
at least two sides have the same length
5m
9 in
9 in
5m
Properties of an Isosceles Triangle
 Has at least 2 equal sides
 Has 2 equal angles
 Has 1 line of symmetry
Parts of an Isosceles Triangle:
Parts of an Isosceles Triangle:
The vertex angle
is the angle
between the two
congruent sides
Parts of an Isosceles Triangle:
The base angles
are the angles
opposite to the
congruent sides
Parts of an Isosceles Triangle:
The base is the
side opposite to
the vertex angle
Isosceles Triangle Theorem
If a triangle is isosceles, then base angles
are congruent.
If
then
Isosceles Triangle Theorem
If a triangle is isosceles, then base angles
are congruent.
If
then
Converse of Isosceles Triangle Theorem
If a triangle has two congruent angles,
then it is an isosceles triangle.
If
then
Equilateral Triangle
all three sides are congruent
7 ft
7 ft
7 ft
Equilateral Triangle Theorem
An equilateral triangle is equiangular, and
an equiangular triangle is equilateral.
Homework
Workbook
1.5, 4.1 & 4.2
All