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Congruent TrianglesCongruent TrianglesStage 6 - Year 11Stage 6 - Year 11

Mathematic(Preliminary)

2

Two triangles are congruent if they are both the same size and shape.

For Example

6cm 6cm8cm 8cm70o 70o

7cm 7cm75o 75o35o 35o

Congruent Triangles 1

3

Two triangles are congruent if.All the three Sides of the

triangles are equal in length.

SSS6cm 6cm8cm 8cm

7cm 7cm

Congruent Triangles 2

4

Two triangles are congruent if.Two pairs of corresponding Sides

and the included Angle are equal.SAS

6cm 6cm8cm 8cm70o 70o

Congruent Triangles 3

5

Two triangles are congruent if.Two pairs of Angles and any pair

of corresponding Sides are equal.AAS

8cm 8cm70o 70o

75o 75o

Congruent Triangles 4

6

Two triangles are congruent if.Both have a Right angle. The Hypotenuses

and one pair of corresponding Sides are equal.RHS

8cm

7cm

8cm

7cm

Congruent Triangles 5

7

Example 1

A

B

C10cm

3.4cm9.4cm

P

Q

R10cm

3.4cm9.4cm

AB = PQ (Corresponding Sides)BC = QR (Corresponding Sides)AC = PR (Corresponding Sides)

Therefore Congruent by SSS

Congruent Triangles 6

8

Example 2

A

B

C

3.4cm9.4cm

P

Q

R

3.4cm9.4cm

AB = PQ (Corresponding Sides)BC = QR (Corresponding Sides)B = Q (Included angle)

Therefore Congruent by SAS

Congruent Triangles 7

9

Example 3

A

B

C10cm

70o

20o

P

Q

R10cm

70o

20o

A = P (Corresponding Angles)C = R (Corresponding Angles)AC = PR (Corresponding Sides)

Therefore Congruent by AAS

Congruent Triangles 8

10

Example 4

A

B

C10cm

3.4cm

P

Q

R10cm

3.4cm

B = Q = 90o (Right Angle)AC = PR (Hypotenuse)BC = QR (Corresponding Sides)

Therefore Congruent by RHS

Congruent Triangles 9