[3 marks sum]

Question 13 Marks

Part of a geometrical figure is given in each of the diagram below. Complete the figures so that both the X-axis and the Y-axis are lines of symmetry of the completed figure.

Give the geometrical name of the completed figure.
(You may use graph paper if required).
Freehand sketches would be sufficient.

Answer

The geometrical name of the completed figure is Square.

The name of the completed figure is Circle.

The name of the completed figure is Rhombus.

The name of the completed figure is Rectangle.

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Question 23 Marks

A quadrilateral ABCD has exactly one axis of symmetry, which is not a diagonal. Show that the quadrilateral is an isosoeles trapezium.

Answer

Consider a quadrilateral ABCD.
Let m be a line which is not a diagonal of quad. ABCD.
Let the quad. ABCD have this line only as its axis of symmetry.
Then A, B and D, C are the two pairs of points each pair symmetric w.r.t., line m.
∴ Line m is the perpendicular bisector of AB as well as DC.
⇒ AB || DC ...(1)
Also AD and BC are symmetric w.r.t., line m.
∴ AD = BC ...(2)
In view of (1) and (2), quadrilateral ABCD is an isosceles trapezium.
Hence proved.

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Question 33 Marks

Use a ruler and compass only in this question.
Construct the quadrilateral ABCD in which AB = 5 cm, BC = 7 cm and angle ABC = 120°, given that AC is its only line of symmetry.

Answer

Steps of construction :
(1) Draw BC = 7 cm and at B make ∠ABC = 120°
(2) With B as centre and radius = 5 cm, cut BX at A.

(3) With A as centre and radius = 5 cm draw an arc and with C as centre and radius = 7 cm draw another arc. The arcs meet at D.
Thus ABCD is the required quadrilateral.

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Mathematics [3 marks sum]

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