New

New

Year 8

# Problem solving with constructions

I can use my knowledge of constructions to solve problems.

New

New

Year 8

# Problem solving with constructions

I can use my knowledge of constructions to solve problems.

## Lesson details

### Key learning points

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

### 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.

### 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.

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.

Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Video

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## Starter quiz

Download starter quiz

### 6 Questions

Q1.

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

Correct Answer: 165

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)?

Correct Answer: 2640, 2640 cm²

2640, 2640 cm²

Q3.

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

15°

Correct answer: 30°

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 $$w$$.

120°

150°

210°

Correct answer: 240°

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.

Correct Answer: 390, 390 cm², 390cm², 390 cm squared, 390cm squared

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.

Correct Answer: 27, 27 cm², 27cm², 27 cm squared, 27cm squared

27, 27 cm², 27cm², 27 cm squared, 27cm squared

## Exit quiz

Download exit quiz

### 6 Questions

Q1.

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

Correct Answer: 5, 5 times, five, five times

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?

Correct answer: equilateral triangle

equilateral triangle

isosceles triangle

Correct answer: scalene triangle

scalene triangle

Correct answer: rhombus

rhombus

parallelogram

Q3.

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

Correct answer: kite

kite

Correct answer: parallelogram

parallelogram

square

Correct answer: trapezium

trapezium

Correct answer: pentagon

pentagon

Q4.

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

Correct answer: Formed from the intersections of two congruent circles.

Formed from the intersections of two congruent circles.

Correct answer: Formed from intersections of different pairs of 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.

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

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?

AE

Correct answer: BE

BE

CG

Correct answer: CF

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)?

Correct Answer: 56.5, 56.5 cm, 56.5cm

56.5, 56.5 cm, 56.5cm

## Additional material

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