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In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10cm, CD = 5cm, AX = 8cm and BX = 6cm.
Use similar triangles to calculate DX.
7) A solid cylinder with radius 1.6cm is attached to the hemisphere to make a toy.
The total volume of the toy is 300cm3.
A mathematically similar toy has volume 19 200cm3.
Calculate the radius of the cylinder for this toy.
8) The diagram shows two cylinders, A and B.
Cylinder A has a height 1.6m and radius 0.56m.
Cylinder B is mathematically similar to cylinder A.
The height of cylinder B is 0.6m.
Work out the radius of cylinder B.
9)
PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.
Explain why triangle PQR is similar to triangle PUT.
Give a reason for each statement you make.
10)
A,B,C and D are points on the circle, centre O.
M is the midpoint of AB and N is the midpoint of CD.
OM = ON
Explain, giving reasons, why triangle OAB is congruent to triangle OCD.