Congruence

The diagram shows a rectangle ABCD with diagonal AC.

Complete each statement to show that triangle ABC is congruent to triangle ADC.

Angle ADC = angle........ because both angles are 90°.

Side AD = side........ because opposite sides of a rectangle are equal.

Side CD = side........ because........

The above three statements show that triangle ABC is congruent to triangle ADC because

ABC is an equilateral triangle. BD is perpendicular to AC.

Prove that triangle ABD is congruent to triangle CBD.

The measurements, in centimetres, of two triangles are shown in the table.

Are the two triangles mathematically similar? Show how you decide.

Are these two triangles definitely congruent? Give a reason.

P, Q, T and V are points on the circumference of a circle. TV is a diameter of the circle. M is a point on PQ such that PM = MQ.

Complete these sentences to show that triangle TMP is congruent to triangle TMQ.

Side PM = side MQ because it is given to you.

Angle PMT = angle........ because........

Triangle TMP is congruent to triangle TMQ because........

On the grid are seven triangles, labelled A to G.

Complete each statement by writing the letter of the correct triangle.

Triangle A is congruent to triangle........

Triangle B is mathematically similar to triangle........

In each row of the table there are two triangles.

State whether the two triangles are congruent or not. If they are congruent state a reason from SSS, SAS, ASA or RHS.

A pattern is made from four congruent right-angled triangles.

The line AC is parallel to the x-axis. The point A has coordinates (4, 9) and the point B has coordinates (17, 12).

Work out the coordinates of point C and point D.

A pattern is made from four congruent right-angled triangles.

The line AC is parallel to the x-axis. The point A has coordinates (4, 9) and the point B has coordinates (17, 12).

Work out the coordinates of point C and point D.

In the diagram, AB and DC are parallel lines of equal length.

Prove that angle DAB = angle BCD.

Are these two triangles definitely congruent? Give a reason.

Prove that these two triangles are congruent.

Are these two triangles definitely congruent? Give a reason.

Prove that these two triangles are congruent.

The diagram below shows two triangles.

Prove that triangle ABC is congruent to triangle ACD.

The diagram below shows two triangles.

Prove that triangle ABC is congruent to triangle ACD.

ABCD is a quadrilateral. AD = AB and CD = CB.

Prove that angle ADC is equal to angle ABC.

Triangles P and Q are right-angled.

Show that the two shorter sides in triangle P have the same lengths as the two shorter sides

in triangle Q.

Explain why the two triangles are congruent.

A and B are points on the circumference of a circle, centre O. CA and CB are tangents to the circle.

Prove that triangle OAC is congruent to triangle OBC.