Shape Booster 6 Similar Shapes

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1 Shape Booster 6 Similar Shapes Check: 85T) The two triangles are similar. 5cm y x 37.8cm 8cm 43.2cm a) Work out the size of x. b) Work out the size of y. a) x = 27cm b) y = 7cm

2 Learn: Maths Watch Reference 123

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4 1) The diagram shows two quadrilaterals that are mathematically similar. B P 8 cm Q A 21 cm S 4 cm R D 14 cm C a) Calculate the length of AB b) Calculate the length of PS 2) SV is parallel to TU. RST and RVU are straight lines. RS = 9 cm, ST = 3 cm, TU = 7 cm, RV = 6 cm Calculate the length of VU. R 9 cm 6 cm 3 cm S V T 7cm U 3) BE is parallel to CD. ABC and AED are straight lines. AB = 4 cm, BC = 6 cm, BE = 5 cm, AE = 4.4 cm a) Calculate the length of CD. A b) Calculate the length of ED. 4 cm 4.4 cm B E 6 cm 5 cm C D Model Exam Questions:

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10 85S) BE is parallel to CD Find the length of BC. A Grade C Clip 123 BC = 8cm 10cm B 12cm E x C 21.6cm D Shape Booster 7 Right Angle Trigonometry Check: 3T) Work out the lengths or angles indicated by the letters a to d. a 25cm b 8cm a = 23.2cm b = Grade B 13cm c = 61.8cm d = 64.6

11 25cm b 8cm a = 23.2cm b = cm c = 61.8cm c 50cm 36 42cm d Learn: 18cm Maths Watch Reference 140 This topic involves right angle triangles. Questions will look very similar to Pythagoras questions but angles are involved. The key steps are: (1) Label the sides of the triangle Hypotenuse (side opposite the right angle), Opposite (side opposite the angle), Adjacent (the third side) (2) Cross out which side is not involved (has nothing labelled) (3) Decide which trig ratio (sin, cos or tan) (4) Substitute the values in the ratio (5) Round your answer as stated in the question These steps are explained below.

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15 1) PQR is a right-angled triangle. PR = 11 cm. QR = 4.5 cm Angle PRQ = 90 Q 4.5 cm Work out the value of x. Give your answer correct to 1 decimal place. P x 11 cm R 2) AC = 14 cm. Angle ABC = 90 Angle ACB = 34 A 14 cm Calculate the length of BC. Give your answer correct to 3 significant figures. B 34 C 3) PQR is a right-angled triangle. PQ = 18 cm. QR = 8.4 cm Angle PRQ = cm Q 8.4 cm Work out the value of x. Give your answer correct to 1 decimal place. P x R 4) AB = 23 cm. Angle ABC = 90 Angle ACB = 21 Calculate the length of AC. Give your answer correct to 3 significant figures. 23 cm A B 21 C 5) A lighthouse, L, is 3.4 km due West of a port, P. A ship, S, is 1.8 km due North of the lighthouse, L. Calculate the size of the angle marked x. Give your answer correct to 3 significant figures. S N 1.8 km N L 3.4 km x P Model Exam Questions: Page 140

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20 3S) Work out the lengths or angles indicated by the letters e to h. 13cm 15cm e f e = 56.9 f = 24.5cm 23cm 32 g = 21.3cm h = 54.1 h 14 g 22cm 19.6cm 24.2cm Shape Booster 8 Simple Circle Theorems Check: Learn: Maths Watch Reference 150 There are a number of circle Theorems this resource focuses on 5 of them. You will need to state the theorem as well as stating the missing angle.

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27 Confirm: 85T) The two triangles are similar. 8cm 5cm y x 37.8cm 16cm 8cm a) Work out the size of x. b) Work out the size of y. 43.2cm a) x = 27cm b) y = 7cm

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