Congruent and similar figures
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1 TUNT OM ongruent and similar figures Time allowed: 5 minutes. Name: art A: 15 multiple-choice questions (30 marks) art : 1 free-response questions (70 marks) art A 15 multiple-choice questions 2 marks each: 30 marks ircle the correct answer. 1 Which transformation(s) is used on figure? A rotation and reflection rotation only translation and rotation translation only 2 If these two triangles are congruent, which side in ΔWXY matches with side KL? L K A YX WX K WY 3 Which angle in ΔKL above matches with X? A Y K L imilar figures have: A matching sides equal the same shape but not the same size the same size but not the same shape the same shape and size 5 ongruent figures have: A the same size but not the same shape the same shape but not the same size the same shape and size matching angles supplementary If these two kites are similar, find r. 15 A Y r W X 20 7 Of the four triangles below, which two are congruent? A I and II II and IV I and IV I and III I III 8 Which one of the following scale factors shows a reduction? A If ΔA and ΔA are A congruent, which angle is equal to A? A A A A A 10 onsider these two statements: 1 All circles are similar 2 All squares are Which statement(s) is true? A tatement 1 only tatement 2 only oth statements 1 and 2 Neither statement is true 11 If KLM and NO are congruent quadrilaterals, which angle in KLM matches with? 3 cm M A L 11 cm II IV K L 11 cm N K M 3 cm O 1
2 TUNT OM ΔT has been reduced to ΔUWV. What was the scale factor? ongruent and similar figures continued U 17 ( marks) eflect each figure across the line. a 1 cm 10 cm cm T 1 A What is the length of UW in the diagram above? A 7.. cm 8 cm. 1 If these parallelograms are similar, find x. W cm V b A Which congruent triangle test can be used to prove that ΔT ΔNLM? A H cm T x AA A art 1 free-response questions 70 marks how working where appropriate. L N 12 cm 1. M 18 (2 marks) otate H 90 clockwise about point. H 19 ( marks) a onstruct a triangle UVW that is congruent to Δ. cm 1 (2 marks) Translate units left, 3 units up. 0 cm 2
3 TUNT OM ongruent and similar figures continued b Use a scale factor of to construct a triangle XYZ that is similar to Δ b Is it possible to draw another rightangled triangle with two shorter sides 2 cm and cm that is not congruent to the one drawn in a? Illustrate with a diagram. 20 ( marks) Out of these triangles: A 23 (2 marks) nlarge this figure by a scale factor of 1.5. a which two are congruent? b which two are similar? c what is the scale factor between the two similar triangles? 21 ( marks) These two quadrilaterals are congruent. 2 ( marks) A wide-screen television set has a screen of dimensions by 30 cm. d 30 cm 1 a Use a scale factor of -- to construct a scale drawing of the television screen. a Name all pairs of matching sides. b Name all pairs of matching angles. b y measurement and calculation, find the length of the television screen s diagonal, d. 22 ( marks) a raw a right-angled triangle with two shorter sides 2 cm and cm. c Use ythagoras theorem to find d. 3
4 TUNT OM (8 marks) These two pentagons are similar. A 2 cm 3 cm 9 cm a What is the scale factor? ongruent and similar figures continued b Which angle in HI is equal to? I x H b What is the scale factor? c y measurement and calculation, find the height of the tree, h, to the nearest 0.1 metre. 28 (2 marks) Lena used similar triangles to calculate w, the width of the river. ind the value of w. c Which side in A is equal to? 30 m w d ind the value of x, the length of H. 15 m 18 m 2 ( marks) ind the value of the pronumeral in each pair of similar figures. a x b (10 marks) In the quadrilateral A, A = and A. A y c p 3 a Name the pair of equal alternate angles in the diagram and mark them ( marks) a Use the scale 1 cm : cm to construct a scale drawing of this 25 diagram. 2 m h b If ΔA and ΔA are congruent, i which side is equal to A? ii which angle is equal to A? iii which angle is equal to? c What type of quadrilateral is A? N O TT. Use the back of the page for extra working space.
5 TUNT OM
6 TUNT OM Answers 1 A ' ' 17 a b ' ' 18 b H ' ' H' 19 Teacher to check 20 a and b A and c a =, =, =, = b =, =, =, = 22 a Teacher to check b No 23 ongruent and similar figures continued 9 2 a b d = 3. c d = 3.53 cm 7. 1 cm 25 a 3 b c d cm 2 a.2 b 7.5 c a b 1 -- c 11.2 m 25 cm m 29 a A b i ii A iii c parallelogram
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