Congruent TrianglesCongruent Triangles

Mathematic

2

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

For Example

6cm 6cm8cm 8cm70o 70o

7cm 7cm75o 75o35o 35o

3

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

triangles are equal in length.SSS

6cm 6cm8cm 8cm

7cm 7cm

4

Two triangles are congruent if.Two pairs of corresponding Sides and the included Angle are

equal.SAS6cm 6cm8cm 8cm

70o 70o

5

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

equal.AAS8cm 8cm

70o 70o

75o 75o

6

Two triangles are congruent if.Both have a Right angle. The Hypotenuses and one pair of corresponding Sides are

equal.RHS8cm

7cm

8cm

7cm

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

8

Example 2

A

B

C3.4cm9.4cm

P

Q

R3.4cm9.4cm

AB = PQ (Corresponding Sides)BC = QR (Corresponding Sides)B = Q (Included angle)Therefore Congruent by SAS

9

Example 3

A

B

C10cm

70o

20oP

Q

R10cm

70o

20o

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

Therefore Congruent by AAS

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