Starter quiz
- Alex rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?
- The hypotenuse of the triangle is side P ✓
- The hypotenuse of the triangle is side Q
- The hypotenuse of the triangle is side R
- Side R has length of 60 units. ✓
- Side R has length of 69.64 units.
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- The perimeter of this right-angled triangle is ______ cm.
- '182' ✓
- Adhesive tape is placed along the two diagonals of this rectangular picture frame. How much adhesive tape is needed, rounded to the nearest cm? ______ cm of tape.
- '186' ✓
- Andeep and Sofia need to split a 3.6 metre roll of adhesive tape in the ratio 7 : 5. The length of the adhesive tape that Andeep receives is ______ centimetres.
- '210' ✓
- These two triangles are similar to each other. The side marked cm is ______ cm long.
- '64' ✓
- An isosceles triangle has an angle of 22°. Which of these are possible sizes of one of the other angles?
- 11°
- 22° ✓
- 45°
- 79° ✓
- 136° ✓
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Exit quiz
- These two triangles are similar to each other and are both in the same orientation. The length of the hypotenuse marked is ______ cm.
- '40' ✓
- The area of this triangle is ______cm².
- '120' ✓
- Which of these statements are correct for this triangle?
- You need to use Pythagoras' theorem to find the size of angle .
- You do not need to use Pythagoras' theorem to find the size of angle . ✓
- ° = 27°
- ° = 43° ✓
- ° = 47°
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- Which of these statements are correct for this triangle?
- The perimeter of this triangle is 16 + 25.4 + 19.7 = 61.1 cm (to 1 d.p.). ✓
- The perimeter of this triangle is 16 + 25.4 + 25.4 = 92.4 cm (to 1 d.p.).
- The area of this triangle is 158 cm² (to the nearest cm²). ✓
- The area of this triangle is 203.2 cm² (to 1 d.p.).
- = 180° − 90° − 51° = 39°.
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- Each square is 1 unit in length. The shortest distance from point A to point B is ______ units (rounded to 2 d.p.).
- '10.05' ✓
- Point C is at the coordinate (12, 3). The perimeter of a triangle whose vertices are at points A, B, and C is ______ units (to the nearest unit).
- '32' ✓
Worksheet
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Presentation
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Lesson Details
Key learning points
- Right-angled triangles can be seen in real-life (e.g. ladder against a vertical wall).
- A ratio table can help you find the scalar and functional multipliers in similar shapes.
- It can be initially difficult to identify whether Pythagoras' theorem can be used.
Common misconception
Every question that has a right-angled triangle must use Pythagoras' theorem to be solved.
It is easy to get into a habit of using Pythagoras' theorem when learning the topic, but it is likely you have seen several maths problems in the past with right-angled triangles, which ask to find areas and angles, without using Pythagoras' theorem.
Keywords
Pythagoras’ theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
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