Introduction to Geometry – Congruent Angles

Every angle has two sides ( or legs ) created by rays.

In this example the legs are AD and AE.

A

D

E

Introduction to Geometry – Congruent Angles

Every angle has two sides ( or legs ) created by rays.

In this example the legs are AD and AE.

The measure of the angle “r” is in degrees.

A

D

E

r

Introduction to Geometry – Congruent Angles

Every angle has two sides ( or legs ) created by rays.

In this example the legs are AD and AE.

The measure of the angle “r” is in degrees.

“A” is the vertex of the angle.A

D

E

r

Introduction to Geometry – Congruent Angles

Every angle has two sides ( or legs ) created by rays.

In this example the legs are AD and AE.

The measure of the angle “r” is in degrees.

“A” is the vertex of the angle.

In geometry, figures are congruent if :

- they have the same angle

- they lie on the same lines

- they pass through the same points

A

D

E

r

Introduction to Geometry – Congruent Angles

Every angle has two sides ( or legs ) created by rays.

In this example the legs are AD and AE.

The measure of the angle “r” is in degrees.

“A” is the vertex of the angle.

In geometry, figures are congruent if :

- they have the same angle

- they lie on the same lines

- they pass through the same points

So two angles could be congruent even though

their rays have different lengths.

A

D

E

r

A

B

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Definition – angles that lie on the same lines are congruent

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Definition – angles that lie on the same lines are congruent

You can see the angles lie on the same lines…

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Definition – angles with legs that pass through the same points are congruent

BA D

C

E

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Definition – angles with legs that pass through the same points are congruent

You can see the angles pass through the same points…

BA D

C

E

EADCAB

When naming angles using points, the vertex is in the middle

Introduction to Geometry – Congruent Angles

The symbol for congruence is ≡ .

Sides can be congruent.

Angles can be congruent.

Figures can be congruent.

EFAB

BA

DEFABC

Definition – angles with legs that pass through the same points have the same measurement.

BA D

C

E

EADCAB 120EAD then ,120 If CAB

Introduction to Geometry – Congruent Angles

Angle congruence theorems :

ANGLE IDENTITY Theorem :

- Any angle is congruent to itself

A

CABCABC

B

Introduction to Geometry – Congruent Angles

Angle congruence theorems :

ANGLE IDENTITY Theorem :

- Any angle is congruent to itself

RIGHT ANGLE CONGRUENCE Theorem :

- Any two right angles are congruent

- a right angle = 90°

A

C

B

ABCABC

B

C

AED

F

DEFABC

Introduction to Geometry – Congruent Angles

Angle congruence theorems :

ANGLE IDENTITY Theorem :

- Any angle is congruent to itself

RIGHT ANGLE CONGRUENCE Theorem :

- Any two right angles are congruent

- a right angle = 90°

STRAIGHT ANGLE CONGRUENCE Theorem :

- any two straight angles are congruent

- a straight angle is a straight line and = 180°

A

C

B

ABCABC

B

C

AED

F

DEFABC

QP R

Y ZX

PQRXYZ