Problem solving with constructions

Maths

The constructions covered in this unit are built on in the future unit. In the future unit, pupils construct triangles and construct diagrams following specific restrictions.

The prior unit gave pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In this unit, pupils will use the geometrical properties of a rhombus to perform various constructions. 

Constructions

In this six-petal flower construction, at how many points does circle A intersect with at least one other circle?

Which of these polygons can be formed by joining up combinations of intersections between any line segment or circle?

Formed from the intersections of two congruent circles.

Formed from intersections of different pairs of congruent circles.

It can be formed from the intersections of any two circles.

At least one circle must have its centre at the midpoint of a line segment.

All circles must have their centres at the endpoints of a line segment.

Which of these statements is true about the construction of a perpendicular bisector?

Which two pairs of points need to be joined with a line segment to find the fourth point in the kite?

This "crescent moon" logo can be formed using the construction of an equilateral triangle that uses two congruent circles of radius 9 cm. What is the perimeter of this logo (in cm, rounded to 1 dp)?

This quadrilateral is a rhombus. Find the value of $$a+b+c$$.

This triangle is reflected with the line of reflection at its base side. The resultant quadrilateral is a rhombus. What is the area of this rhombus (in cm²)?

This hexagon is regular. Find the size of angle $$v$$, in degrees.

The triangle is equilateral, with two angle bisectors extending from the bottom two angles of the equilateral triangle and intersecting inside the triangle. Find the size of angle $$w$$.

This diagram shows a kite enclosed by a rectangle. If the rectangle has an area of 780 cm², find the area of the kite, in cm².

This kite has an area of 270 cm². What is the area of the shaded region: the right-angled triangle on the top, right of the kite? Give your answer in cm².

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