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Congruent triangles

- Unit 4

Classifying ?s

Congruent ?s

Triangles

Proving ?s congruent

Angles in ?s

Triangle

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

Classifying by angles

- Right
- Obtuse
- Acute

1 right angle

3 acute angles

1 obtuse angle

Equiangular Triangle

3 equal angles

- Special acute triangle

Classifying by sides

- Scalene
- Isosceles
- Equilateral

3 ? sides

No ? sides

2 ? sides

Parts of a right triangle

Hypotenuse

Leg

Leg

Parts of an isosceles triangle

Leg

Leg

Vertex angle

Base angle

Base angle

Base

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

Exterior Interior Angles

C

remote interior angles

exterior angle

interior angle

A

D

B

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

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

Corollary 4.1

- the acute angles of a right triangle are

complementary

E

m?D m ?E 90

D

F

Corollary 4.2

- there can only be 1 right angle or obtuse angle

in a triangle

Corresponding parts

- parts correspond (match up) in the same order

that they are written in a statement

Corresponding parts

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

Definition of ? ?s (CPCTC)

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

?ABC ? ?DEF (CPCTC)

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

C

F

B

A

E

D

Theorem 4-4

- Congruence of triangles is
- reflexive
- symmetric
- transitive

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

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