Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays....
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Transcript of Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays....
![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/6.jpg)
Introduction to Geometry – Congruent Angles
The symbol for congruence is ≡ .
![Page 7: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/9.jpg)
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…
![Page 10: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/11.jpg)
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
![Page 12: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/12.jpg)
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
![Page 13: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/13.jpg)
Introduction to Geometry – Congruent Angles
Angle congruence theorems :
ANGLE IDENTITY Theorem :
- Any angle is congruent to itself
A
CABCABC
B
![Page 14: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/14.jpg)
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
![Page 15: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072005/56649cee5503460f949bc668/html5/thumbnails/15.jpg)
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