Congruence

In the following diagram:

• CB and DE are parallel • CE and BD are straight lines • CA = AE.

Prove that triangles ABC and ADE are congruent.

You must show all your working and explain your reasoning.

In the following diagram, the lines AC and BD bisect each other.

Prove that triangles ABE and CDE are congruent.

You must state the condition of congruence.

In the diagrams below, ABCD is a square.

Triangles ABE and KLM are congruent.

Calculate the area of the square ABCD.

In the triangle EFH below:

• G is the midpoint of FH, • EG and FH are perpendicular.

Prove that EFG and EHG are congruent triangles.

You must state the condition of congruence.

Circle either TRUE or FALSE for each statement given below.

In the following diagram, AE and BD are straight lines and BC = CE.

Is it possible to conclude that triangles ABC and DEC are congruent?

You must show all your working and explain your decision.

SSS, SAS, ASA and RHS are notations used to describe the conditions required to prove that two triangles are congruent. [S ≡ Side, A ≡ Angle, R ≡ Right angle and H ≡ Hypotenuse.]

The following triangles are not drawn to scale. For each pair of triangles, circle the correct statement.