12 original questions, 28 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
Here are the side lengths of four triangles.
Triangle A: 5 cm, 7 cm, 9 cm
Triangle B: 5 cm, 7 cm, 8 cm
Triangle C: 9 cm, 7 cm, 5 cm
Triangle D: 5 cm, 6 cm, 9 cm
Write down the letters of the two triangles that are congruent to each other.
Lena says, "If two triangles have the same three angles, they must be congruent."
In triangles PQR and XYZ,
PQ = XY = 6 cm
angle PQR = angle XYZ = 40°
QR = YZ = 8 cm
The two triangles are congruent.
Write down the congruence condition that shows the triangles are congruent.
The diagram shows triangle PQR and triangle XYZ.
Are the two triangles congruent? Give a reason for your answer.
Triangle ABC is congruent to triangle DEF.
A corresponds to D, B corresponds to E and C corresponds to F.
AB = 7 cm, BC = 9 cm, angle ABC = 48° and angle BCA = 71°.
Rectangle A measures 4 cm by 6 cm.
Rectangle B is mathematically similar to rectangle A. The shorter side of rectangle B is 10 cm.
Triangle ABC is similar to triangle PQR.
AB corresponds to PQ, and BC corresponds to QR.
AB = 6 cm, PQ = 9 cm and BC = 8 cm.
Work out the length of QR.
Triangles ABC and PQR are mathematically similar.
Angle ABC = angle PQR and angle BCA = angle QRP.
Jamal is 1.6 m tall. At 4 pm his shadow is 2 m long.
At the same time, a flagpole next to him casts a shadow 9 m long.
The sun makes similar triangles with Jamal and with the flagpole, as shown in the diagram.
Work out the height of the flagpole.
ABCD is a kite in which AB = AD and CB = CD.
The diagonal AC is drawn.
Prove that triangle ABC is congruent to triangle ADC.
The straight lines AD and BC cross at M.
AM = MD and BM = MC.
Prove that triangle ABM is congruent to triangle DCM.
In triangle ABC, D is a point on AB and E is a point on AC.
DE is parallel to BC.
AD = 4 cm, DB = 6 cm and DE = 5 cm.
Work out the length of BC.
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.