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      Problem solving with constructions

      Lesson details

      Learning outcome

      I can use my knowledge of constructions to solve problems.

      Key learning points

      1. Shapes made from triangles can be constructed.
      2. By investigation it is possible to accurately construct multiple polygons.
      3. Shortest distances can be found using constructions with perpendicular lines.

      Keywords

      • Bisect - To bisect means to cut or divide an object into two equal parts.

      • Rhombus - A rhombus is a parallelogram where all sides are the same length.

      Common misconception

      You always need to draw circles that are the same size to construct any polygon.

      Some polygons, such as kites, require you to construct two circles of different size, as long as they still intersect at two points.

      Teacher tip

      Whilst students are exploring possible shapes that can be found on constructions, providing the "six-petal flower construction" additional material gives multiple copies of premade constructions for students to draw over.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      This quadrilateral is a rhombus. Find the value of $$a+b+c$$.

      An image in a quiz
      Correct Answer: 165

      Q2.
      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)?

      An image in a quiz
      Correct Answer: 2640, 2640 cm²

      Q3.
      This hexagon is regular. Find the size of angle $$v$$, in degrees.

      An image in a quiz
      15°
      Correct answer: 30°
      45°
      60°
      90°

      Q4.
      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 $$w$$.

      An image in a quiz
      120°
      150°
      210°
      Correct answer: 240°
      300°

      Q5.
      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.

      An image in a quiz
      Correct Answer: 390, 390 cm², 390cm², 390 cm squared, 390cm squared

      Q6.
      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.

      An image in a quiz
      Correct Answer: 27, 27 cm², 27cm², 27 cm squared, 27cm squared

      6 Questions

      Q1.
      In this six-petal flower construction, at how many points does circle A intersect with at least one other circle?

      An image in a quiz
      Correct Answer: 5, 5 times, five, five times

      Q2.
      Which of these polygons can be formed by joining up combinations of intersections between any line segment or circle?

      An image in a quiz
      Correct answer: equilateral triangle
      trapezium
      Correct answer: scalene triangle
      Correct answer: rhombus
      square

      Q3.
      Which of these polygons can be formed by joining up combinations of intersections between any line segment or circle?

      An image in a quiz
      Correct answer: kite
      Correct answer: parallelogram
      square
      Correct answer: trapezium
      Correct answer: pentagon

      Q4.
      Which of these statements is true about the construction of a perpendicular bisector?

      Correct answer: It is formed from the intersections of two congruent circles.
      Correct answer: It is 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.
      Correct answer: All circles must have their centres at the endpoints of a line segment.

      Q5.
      Which two pairs of points need to be joined with a line segment to find the fourth point in the kite?

      An image in a quiz
      AE
      Correct answer: BE
      CG
      Correct answer: CF
      BC

      Q6.
      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)?

      An image in a quiz
      Correct Answer: 56.5, 56.5 cm, 56.5cm

      To help you plan your 8 maths lesson on: Problem solving with constructions, download all teaching resources for free and adapt to suit your pupils' needs...