Download Congruent Figures ppt.

Congruent Figures
Congruent figures have the same size and
shape. When two figures are congruent,
you can slide, flip, or turn one so that it fits
exactly on the other.
turn
slide
flip
Congruent polygons have congruent
corresponding parts - their matching sides
and angles. When naming congruent
polygons, corresponding vertices must be
listed in the same order.
A
D
B
F
E
C
G
ABCD  EFGH
H
Congruent polygons have congruent
corresponding parts - their matching sides
and angles. When naming congruent
polygons, corresponding vertices must be
listed in the same order.
A
D
B
AB  EF
F
E
C
G
ABCD  EFGH
H
A  E
BC  FG B  F
CD  GH C  G
DA  HE D  H
Third Angles Theorem
If two angles of one triangle are congruent to
two angles of another triangle, then the third
angles are congruent.
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
A
B
Statements
1. A  D, B  E
2. mA = mD, mB = mE
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
4. mA + mB + mC = mD + mE + mF
5. mC = mF
6. C  F
D
Reasons
CE
F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
A
B
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
4. mA + mB + mC = mD + mE + mF
5. mC = mF
6. C  F
D
CE
F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
4. mA + mB + mC = mD + mE + mF
5. mC = mF
6. C  F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
3. The sum of the interior angles of
a triangle is 180°. (2)
4. mA + mB + mC = mD + mE + mF
5. mC = mF
6. C  F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
3. The sum of the interior angles of
a triangle is 180°. (2)
4. mA + mB + mC = mD + mE + mF
4. Substitution Property (3)
5. mC = mF
6. C  F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
3. The sum of the interior angles of
a triangle is 180°. (2)
4. mA + mB + mC = mD + mE + mF
4. Substitution Property (3)
5. mC = mF
5. Subtraction Property (4, 2)
6. C  F
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
3. The sum of the interior angles of
a triangle is 180°. (2)
4. mA + mB + mC = mD + mE + mF
4. Substitution Property (3)
5. mC = mF
5. Subtraction Property (4, 2)
6. C  F
6. If two angles are equal in
measure, then they are congruent.
(6)
Proof of Third Angles Theorem
Given: A  D, B  E
Prove: C  F
D
A
B
CE
F
Statements
Reasons
1. A  D, B  E
1. Given
2. mA = mD, mB = mE
2. If two angles are congruent, then
they are equal in measure. (1)
3. mA + mB + mC = 180°,
mD + mE + mF = 180°
3. The sum of the interior angles of
a triangle is 180°. (2)
4. mA + mB + mC = mD + mE + mF
4. Substitution Property (3)
5. mC = mF
5. Subtraction Property (4, 2)
2. C  F
2. If two angles of one triangle are
congruent to two angles of another
triangle, then the third angles are
congruent.