Ratios of corresponding sides in harder problems.
16 original questions, 52 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
Rectangle A is 4 cm by 6 cm. Rectangle B is 8 cm by 10 cm.
Sam says, "Each side of rectangle B is 4 cm longer than the matching side of rectangle A, so the rectangles are similar."
Explain why Sam is wrong.
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.
In triangle ABC, angle A = 35° and angle B = 80°.
In triangle DEF, angle D = 80° and angle E = 65°.
Show that triangle ABC is similar to triangle DEF.
A photograph is 15 cm long and 10 cm wide.
The photograph is enlarged to make a print that is mathematically similar to it.
The print is 24 cm long.
Quadrilateral ABCD is similar to quadrilateral PQRS.
AB corresponds to PQ, BC corresponds to QR, CD corresponds to RS and DA corresponds to SP.
AB = 6 cm, PQ = 15 cm and CD = 8 cm.
Triangle ABC is similar to triangle DEF.
AB corresponds to DE, BC corresponds to EF, and AC corresponds to DF.
AB = 5 cm, BC = 7 cm, DE = 7.5 cm and DF = 12 cm.
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.
A vertical post 1.5 m tall casts a shadow 2.4 m long. At the same time a tree casts a shadow 9.6 m long.
The post, the tree and their shadows form two similar right-angled triangles.
Work out the height of the tree.
Triangle ABC is isosceles with AB = AC = 5 cm and BC = 8 cm.
Triangle PQR is similar to triangle ABC with PQ = PR = 12 cm.
Work out the length of QR.
Triangle ABC has AB = 6 cm, BC = 8 cm and CA = 10 cm.
Triangle DEF is congruent to triangle ABC, with D matching A, E matching B and F matching C.
Triangle GHI is similar to triangle ABC, with G matching A, H matching B and I matching C. GH = 9 cm.
AB is parallel to DE.
The straight lines AE and BD cross at the point C.
AC = 9 cm, CE = 6 cm, AB = 12 cm and CD = 5 cm.
In triangle ADE, B is a point on AD and C is a point on AE.
BC is parallel to DE.
AB = 6 cm, BD = 3 cm and BC = 8 cm.
The area of triangle ABC is 24 cm2.
Rectangle A is 8 cm by 5 cm.
Rectangle B is similar to rectangle A and has a perimeter of 52 cm.
Work out the length and width of rectangle B.
In triangle PQR, angle PQR = 90°, PQ = 6 cm, QR = 8 cm and PR = 10 cm.
S is the point on PR such that QS is perpendicular to PR.
Work out the length of QS.
In triangle ABC, D is a point on AB.
Angle ACD = angle ABC.
AC = 8 cm and AD = 4 cm.
Triangle ABC is similar to triangle PQR.
AB = 4 cm, PQ = 10 cm, BC = x cm and QR = (x + 9) cm.
Work out the value of x and the length of QR.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.