Triangles, Quadrilaterals, and Polygons
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Triangles, Quadrilaterals, and Polygons — Free MYP3 Mathematics Practice Questions

1QuestionProperties of Isosceles Equilateral and Right TrianglesConcept Practice
2 marks~3 minCriterion A
An isosceles triangle has two equal sides. One base angle measures 40°40°.

Calculate the vertex angle of the triangle. [2]
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Solutions

2QuestionProperties of Squares Rectangles Parallelograms and TrapeziumsAssessment Practice
5 marks~8 minCriterion C
Quadrilateral ABCDABCD has vertices A(1,2)A(1, 2), B(4,5)B(4, 5), C(7,2)C(7, 2), D(4,−1)D(4, -1).
a
Calculate the slopes of all four sides ABAB, BCBC, CDCD, and ADAD. [2]
b
Explain how your slopes show that ABCDABCD is a parallelogram. [2]
c
Justify whether ABCDABCD is a rectangle. Use co-interior angles in your answer. [1]
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Solutions

3QuestionClassifying Triangles by Sides and AnglesAssessment Practice
6 marks~9 minCriterion D
A surveyor measures a triangular plot of land and records angles of 90°90°, 45°45°, and 45°45°. Her laser tool has a margin of error of ±2°\pm 2° per angle.
a
Describe the type of triangle formed by the angles 90°90°, 45°45°, and 45°45°, classifying it by both angles and sides. [2]
b
Explain how a ±2°\pm 2° measurement error could produce a different triangle. Give one possible set of actual angles and classify that triangle by both angles and sides. [2]
c
Analyse the validity of the surveyor's claim that the plot is exactly right isosceles, given the measurement error. [2]
Question diagram

Solutions

4QuestionProperties of Isosceles Equilateral and Right TrianglesAssessment Practice
6 marks~9 minCriterion B
The table below shows the vertex angle and base angles of five isosceles triangles.

Vertex angle (vv, degrees)20406080100
Base angle (bb, degrees)8070605040
a
Calculate the sum of all three angles for each triangle in the table. [2]
b
Explain why the relationship between the vertex angle vv and base angle bb in any isosceles triangle can be written as b=180−v2b = \dfrac{180 - v}{2}. [2]
c
A student claims that an isosceles triangle with a vertex angle of 36°36° has base angles of 72°72° each, making it a special triangle where the base angle is exactly twice the vertex angle. Analyse whether this claim is correct and explain what is special about this triangle. [2]

Solutions

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