quiz ethan

The figure shows a kite ABCD.

It is given that AC and BD intersects at point 0.

Write down the number of pairs of congruent triangles.

Rectangle P is mapped onto rectangle Q by an enlargement.

Given that the perimeter of rectangle Q is 11.2 cm, calculate the value of h.

A length of 5 cm on a map represents an actual distance of 1 km.

Calculate the area on the map, in square centimetres, which represents an actual area of 6 km²

Three vertical poles of different lengths are arranged as shown in the diagram.

Find the height of the tallest pole.

A craftsman makes a model of a car garage using a scale of 1: 20.

Given that the height of the roof of the model is 40 cm, find the height in metres, of the actual roof.

A craftsman makes a model of a car garage using a scale of 1: 20.

Given that the actual area of the car garage is 60 square metres, find the area of the model of the car garage in square centimetres.

In the diagram, ∆ ABC and ∆ DEF are similar. Calculate the value of x. The dimensions given are in m.

A map has a scale of 2.5 cm to 5 km. The distance between Town A and Town B on the map is 8 cm. Find the

distance, in cm, between Town A and Town B on another map which has a scale of 1: 50 000.

The containers as shown in the diagram are geometrically similar. The height of the smaller container is 9 cm and the height of the larger container is 12 cm.

If the base radius of the smaller container is 2.5 cm, find the base radius of the larger container.

Mathematical Equivalence

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The containers as shown in the diagram are geometrically similar. The height of the smaller container is 9cm and the height of the larger container is 12 cm.

Given that the top of the larger container has a circumference of 64 cm, calculate the circumference of the top of the smaller container.