Congruence and Similarity
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Congruence and Similarity — Free MYP2 Mathematics Practice Questions

1QuestionApplications of Congruence and Similarity in Real LifeConcept Practice
2 marks~3 minCriterion A
Two similar triangular gardens are shown in the diagram. The smaller garden has side lengths of 4 m and 6 m. The larger garden has a corresponding side of 8 m and an unknown side of xx m.
a
Identify the scale factor from the smaller garden to the larger garden. [1]
b
Calculate the value of xx. [1]
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2QuestionTesting for Congruence with Rigid TransformationsAssessment Practice
5 marks~8 minCriterion C
Triangle ABCABC has vertices A(1,2)A(1, 2), B(3,4)B(3, 4), and C(5,1)C(5, 1). Triangle DEFDEF has vertices D(−1,−2)D(-1, -2), E(−3,−4)E(-3, -4), and F(−5,−1)F(-5, -1).
a
State the coordinate rule for a rotation of 180°180° about the origin. [1]
b
Apply this rule to show that triangle ABCABC maps exactly onto triangle DEFDEF. [2]
c
A student claims triangle DEFDEF is the image of triangle ABCABC after a translation of 2 units left and 4 units down, followed by a reflection across the xx-axis. Compare the student's result with the correct image and explain the error in their reasoning. [2]
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3QuestionUnderstanding Congruent ShapesConcept Practice
3 marks~5 minCriterion B
The graph shows the relationship between the side length and the perimeter of a square.
a
Identify the value by which the perimeter increases each time the side length increases by 1 cm. [1]
b
Write a formula for the perimeter PP in terms of the side length ss. [1]
c
A second square has a side length of 6 cm and a perimeter of 24 cm. Compare how well this square fits the relationship shown in the graph. [1]
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4QuestionExploring Similar Shapes and ProportionalityAssessment Practice
5 marks~8 minCriterion D
An architect makes a scale model of a triangular building facade using a scale of 1:201:20. The model's side lengths are 15 cm15\ \text{cm}, 20 cm20\ \text{cm}, and 25 cm25\ \text{cm}.
a
Calculate the actual side lengths of the facade in metres. [2]
b
Explain one reason why the angles of the real facade may not match the model's angles exactly. [1]
c
Compare how a change in the facade's angles could affect the accuracy of the architect's material cost estimate. [2]
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