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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

mA mB mC 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

mDAC mB mC

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

mD 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

- ABCDEF
- AD ABDE
- BE BCEF
- CF ACDF

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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