Congruent triangles

1
Congruent triangles

• Unit 4

2
Classifying ?s
Congruent ?s
Triangles
Proving ?s congruent
Angles in ?s
3
Triangle

• A three sided polygon
• Can be classified 2 ways
• angles
• sides

4
Classifying by angles

• Right
• Obtuse
• Acute

1 right angle
3 acute angles
1 obtuse angle
5
Equiangular Triangle
3 equal angles

• Special acute triangle

6
Classifying by sides

• Scalene
• Isosceles
• Equilateral

3 ? sides
No ? sides
2 ? sides
7
Parts of a right triangle

Hypotenuse
Leg
Leg
8
Parts of an isosceles triangle

Leg
Leg
Vertex angle
Base angle
Base angle
Base
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Triangle Sum Theorem

• The sum of the measures of the angles in a
  triangle is 180

C
m?A m?B m?C 180
B
A
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Exterior Interior Angles

C
remote interior angles
exterior angle
interior angle
A
D
B
11
Exterior Angle Theorem

• The measure of the exterior angle is the sum of
  the measures of the two remote interior angles

C
m?DAC m?B m?C
B
A
D
12
Third Angle Theorem

• If 2 angles in one triangle are congruent to 2
  angles in another triangle, then the 3rd angles
  are congruent

C
E
B
A
F
D
13
Corollary 4.1

• the acute angles of a right triangle are
  complementary

E
m?D m ?E 90
D
F
14
Corollary 4.2

• there can only be 1 right angle or obtuse angle
  in a triangle

15
Corresponding parts

• parts correspond (match up) in the same order
  that they are written in a statement

16
Corresponding parts

• ?ABC??DEF
• A?D AB?DE
• B?E BC?EF
• C?F AC?DF

17
Definition of ? ?s (CPCTC)

• 2 triangles are ?
• if and only if
• their corresponding parts are ?

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?ABC ? ?DEF (CPCTC)

• A ? D AB ? DE
• B ? E BC ? EF
• C ? F AC ? DF

C
F
B
A
E
D
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Theorem 4-4

• Congruence of triangles is
• reflexive
• symmetric
• transitive

20
Included side
a side between 2 angles it is formed by the
angles AB is the included side of angles A B
C
A
B