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Congruence and Similarity — Free MYP1 Mathematics Practice Questions
1QuestionExploring Similar Shapes and ProportionalityConcept Practice
2 marks~3 minCriterion D
A photo measures 6 cm by 9 cm. A poster frame measures 24 cm by 36 cm.
a
Calculate the scale factor used to enlarge the photo to fit the frame. [1]
b
Describe one way the enlarged photo of a person's face might look different from the original. [1]
Solutions
2QuestionTesting for Congruence with Rigid TransformationsAssessment Practice
6 marks~9 minCriterion C
A student flips a triangle over a line to make a second triangle.
a
Name the type of transformation that keeps a shape exactly the same size and shape. [1]
b
Describe one reason why a hand-drawn flip, with no ruler or grid, may not prove the two triangles are congruent. [2]
c
Describe one way using tracing paper and one way using a grid that could give a more reliable check of congruence. [3]
Solutions
3QuestionExploring Similar Shapes and ProportionalityConcept Practice
4 marks~6 minCriterion A
Triangle A has sides of 3 cm, 4 cm, and 5 cm. Triangle B is similar to Triangle A. The side of Triangle B that matches the 5 cm side of Triangle A measures 10 cm.
a
Identify the scale factor from Triangle A to Triangle B. [1]
b
Calculate the length of the side of Triangle B that matches the 3 cm side of Triangle A. [1]
c
Describe how you know the two triangles are similar, using the side lengths of both triangles in your answer. [2]
Solutions
4QuestionExploring Similar Shapes and ProportionalityConcept Practice
2 marks~3 minCriterion B
Three pairs of similar rectangles are shown below.
Pair A: small rectangle 2 cm by 3 cm; large rectangle 4 cm by 6 cm.
Pair B: small rectangle 1 cm by 4 cm; large rectangle 3 cm by 12 cm.
Pair C: small rectangle 2 cm by 5 cm; large rectangle 6 cm by 15 cm.
Pair A: small rectangle 2 cm by 3 cm; large rectangle 4 cm by 6 cm.
Pair B: small rectangle 1 cm by 4 cm; large rectangle 3 cm by 12 cm.
Pair C: small rectangle 2 cm by 5 cm; large rectangle 6 cm by 15 cm.
a
For each pair, calculate the ratio of the large rectangle's side length to the matching side length of the small rectangle. [1]
b
Describe what you notice about the ratios in each pair. [1]
Solutions
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