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Transcript 
Chapter 4
Congruent Triangles
4.1 & 4.6 Triangles and Angles
Triangle: a figure formed by three segments
joining three noncollinear points.
Classification by
SIDES
Equilateral
Classification by
ANGLES
Acute
Isosceles
Equiangular
Scalene
Right
Obtuse
Classification by Sides
• Equilateral Triangle
– 3 congruent sides
• Isosceles Triangle
– 2 congruent sides
• Scalene Triangle
– No congruent sides
Classification by Angles
• Acute
– All angles are acute
• Equiangular
– All angles are congruent
• Right
– One right angle and 2 acute angles
• Obtuse
– One obtuse angle and 2 acute angles
Classify the following triangles
Isosceles
Triangle
Equilateral
Triangle
Scalene
Triangle
Classify the following triangles
65°
58°
130°
57°
Acute scalene
Right
isosceles
Obtuse isosceles
Parts of a Triangle
• A vertex is one of the three points joining
sides of a triangle.
• Two sides sharing a common vertex are
adjacent sides.
Parts of a right triangle
• Legs: the sides that form the
right angle of the triangle
• Hypotenuse: the side
opposite the right angle
Leg
Leg
Parts of an isosceles triangle
• Legs: the two congruent
sides
• Base: the third side
Leg
Leg
Base
Angle Measures of Triangles
• Interior Angles: The three original
angles
• Exterior Angles: The angles adjacent
to the interior angles
Interior Angles
Exterior Angles
Triangle Sum Theorem
• The sum of the measures of
the interior angles of a
triangle is 180°.
C
B
A
mA  mB  mC  180
Corollary to the Triangle Sum
Theorem
• The acute angles of a right
triangle are complementary.
A
2x°
B
x°
mA + mB = 90
x + 2x = 90°
X = 30°
More Practice
Find the measures of the missing angles:
1
1
40°
2
3
56°
95°
42°
m1 = 48°
3
m1 = 50°
45°
1 50° 2
m2 = 40°
m1 = 79°
m3 = 45°
m2 = 51°
m3 = 39°
Exterior Angle Theorem
• The measure of an exterior angle of a
triangle is equal to the sum of the
measures of the two remote interior
angles.
Exterior
Angle
B
m1 = mA + mB
A
1
65°
x + 65 = 2x + 10
x°
(2x + 10)°
x = 55
IsoscelesTriangles
• Base Angles: The two angles in an
isosceles triangle adjacent to the
base
• Vertex Angle: The angle opposite the
base
Base Angle
Base Angle
Base Angles Theorem
• If two sides of a triangle
are congruent, then the
angles opposite them are
congruent.
A
If AB  AC, thenB  C
C
B
Converse to the Base Angles
Theorem
• If two angles of a
triangle are congruent,
then the sides opposite
them are congruent.
IfB  C , then AB  AC
Corollary to the Base Angles
Theorem
• If a triangle is equilateral, then
it is equiangular.
Corollary to the Converse of the
Base Angles Theorem
• If a triangle is equiangular,
then it is equilateral.
Practice Problems
• Find the measure of the missing angles.
B
B
A
50°
m  B=80°
C
A
C
m  A=60°
m  B=60°
m  C=50°
m  C=60°
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