Starter quiz
- Izzy writes down a correct Pythagoras' theorem equation for a triangle. Which of the three sides of this triangle is the hypotenuse?
- side A ✓
- side B
- side C
- impossible to tell
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- Aisha rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?
- The hypotenuse of the triangle is side W
- The hypotenuse of the triangle is side X
- The hypotenuse of the triangle is side Y ✓
- Side W has length of 32 400 units.
- Side W has a length of 180 units. ✓
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- Which of these are correct for this triangle?
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- ✓
- ✓
- (to 1 d.p.) ✓
- (to 1 d.p.)
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- What is the value of , rounded to 2 d.p.? ______.
- '26.38' ✓
- The diagonals of this kite have been drawn on. The value of is ______.
- '8' ✓
- The diagonals of this kite have been drawn on. Which of these statements are correct.
- The two diagonals of a kite intersect to create two acute angles of equal length
- The two diagonals of a kite intersect at right angles ✓
- ✓
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-
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Exit quiz
- On this football pitch, the goalkeeper (at point A) wants to kick the ball to a striker (at point E), however the goalkeeper's longest kick is 91 m. Which of these statements are correct?
- The distance between the goalkeeper and the striker is 49.24 metres.
- The distance between the goalkeeper and the striker is 92.20 metres (to 2 d.p.). ✓
- The distance between the goalkeeper and the striker is 98.49 metres (to 2 d.p.).
- The ball the goalkeeper kicks will reach the striker.
- The ball the goalkeeper kicks will not reach the striker. ✓
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- A factory produces cylindrical saucepans whose maximum base length is 28 cm. What must the minimum integer height of the saucepan be (in cm) so it can fully submerge a spaghetti noodle.
- 15 cm
- 16 cm ✓
- 19 cm
- 28 cm
- 32 cm
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- An archer fires an arrow that travels 20 metres to hit a target that is 9 m above ground. The arrow then drops to the ground. The archer must walk ______ m (to 2 d.p.) to pick up the arrow.
- '17.86' ✓
- An archer fires an arrow at a target 20 m away. The arrow drops 9 m to the ground. Jun uses Pythagoras' theorem to find how far the archer walks to collect the arrow. What assumptions does Jun make?
- The arrow travels in a straight line. ✓
- The speed of the arrow is constant.
- The ground the archer walks on to pick up the arrow is flat. ✓
- The archer fires the arrow from the ground. ✓
- The accuracy of the archer.
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- The captain (at C) passes the ball to the goalkeeper (at A), who then passes to the midfielder (at D), who then passes to a striker (at F). The total distance the ball travelled is ______m (to 2 d.p.).
- '154.45' ✓
- Two bamboo sticks are placed on the diagonal of this kite to support it during high winds. The length of the vertical bamboo stick is ______ cm (to 2 d.p.).
- '189.29' ✓
Worksheet
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Presentation
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Lesson Details
Key learning points
- Within context, it can be difficult to initially identify whether Pythagoras' theorem can be used.
- Pythagoras' theorem may be used if a right-angled triangle can be drawn, even if drawn within a different shape.
- Pythagoras' theorem can be used to check for properties of other shapes involving right-angles.
Common misconception
I need to be given a triangle in order to use Pythagoras' theorem.
You do not need to be given a triangle. It is an important skill to be able to sketch and label a triangle for yourself from given information, or go straight into an algebraic stage of calculation if aware that lengths given are perpendicular.
Keywords
Perpendicular height - The perpendicular height is the perpendicular distance from the base to the opposite vertex.
Pythagoras’ theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).
Hypotenuse - A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.
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