You're viewing free preview questions. Upgrade to access more MYP2 questions.Upgrade
Geometry – Properties of Shape

Geometry – Properties of Shape — Free MYP2 Mathematics Practice Questions

1QuestionClassifying Triangles by Sides and AnglesConcept Practice
3 marks~5 minCriterion A
The graph shows the relationship between the number of sides of a regular polygon and the sum of its interior angles.
a
Identify the increase in the sum of interior angles each time the number of sides increases by 1. [1]
b
Calculate the sum of interior angles for a regular polygon with 9 sides. [1]
c
A regular polygon has a sum of interior angles of 900°. Explain whether it could also be classified as a quadrilateral. [1]
Question diagram

Solutions

2QuestionUnderstanding Interior Angles of PolygonsConcept Practice
3 marks~5 minCriterion B
The table below shows the sum of interior angles for polygons with 3 to 10 sides.

Number of sides345678910
Sum of interior angles (°)180360540720900108012601440
a
Using (n−2)×180°(n-2) \times 180°, calculate the sum of interior angles of a pentagon (n=5n = 5). [1]
b
Describe the relationship between the number of sides and the sum of interior angles shown in the table. [1]
c
A polygon has an interior angle sum of 1800°. Explain how you can find the number of sides, and state your answer. [1]
Question diagram

Solutions

3QuestionCreating Symmetrical DesignsConcept Practice
2 marks~3 minCriterion A
The diagram shows a butterfly design with a dashed vertical line through its centre.
a
State the total number of lines of symmetry in the butterfly design. [1]
b
Identify the orientation of this line of symmetry as vertical, horizontal, or diagonal. [1]
Question diagram

Solutions

4QuestionUnderstanding 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]
Question diagram

Solutions

5QuestionApplications 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]
Question diagram

Solutions

6QuestionDrawing Circles with Compass and RulerConcept Practice
2 marks~3 minCriterion A
The diagram shows a circle with centre OO. Point PP lies on the circumference. Line segment OPOP is drawn.
a
Identify the mathematical name of line segment OPOP. [1]
b
Measure the length of OPOP on the diagram and state your answer in centimetres. [1]
Question diagram

Solutions

7QuestionSolving Problems with Justification and ProofConcept Practice
3 marks~5 minCriterion B
The graph shows the sum of interior angles for regular polygons with 3, 4, 5, and 6 sides.
a
State the sum of interior angles of a triangle. [1]
b
Explain the pattern shown in the graph. [1]
c
Calculate the sum of interior angles of an octagon (8 sides). [1]
Question diagram

Solutions

8QuestionAlternate Interior and Exterior AnglesConcept Practice
2 marks~3 minCriterion A
In the diagram, two parallel lines are cut by a transversal (a line that crosses both parallel lines). One alternate interior angle measures 65°65°.
a
State the measure of the other alternate interior angle. [1]
b
Identify the geometric property that justifies your answer in part (a). [1]
Question diagram

Solutions

9QuestionVertically Opposite and Corresponding AnglesConcept Practice
5 marks~8 minCriterion C
Two straight lines intersect, forming four angles. One angle is 37°37°.

Vertically opposite angles are the equal angles directly across from each other at an intersection.
a
State the size of the angle vertically opposite to 37°37°. [1]
b
Calculate the sizes of the other two angles formed at the intersection. [2]
c
A student claims: "If one angle in a pair of vertically opposite angles is acute (less than 90°90°), the other must also be acute." Using your results, explain whether this claim is correct. [2]
Question diagram

Solutions

10QuestionConstructing and Measuring Angles with ProtractorConcept Practice
5 marks~8 minCriterion B
Two straight lines, ACAC and BDBD, intersect at point OO, forming four angles: ∠AOB=35°\angle AOB = 35°, ∠BOC=145°\angle BOC = 145°, ∠COD=35°\angle COD = 35°, and ∠DOA=145°\angle DOA = 145°.
a
Identify the relationship between ∠AOB\angle AOB and ∠BOC\angle BOC. [1]
b
Calculate ∠COD\angle COD using the straight-line property (angles on a straight line sum to 180°180°). Show your working. [2]
c
Compare ∠AOB\angle AOB and ∠COD\angle COD. Explain why they must always be equal for any two intersecting lines. [2]
Question diagram

Solutions

11QuestionAngle Relationships in Parallel Lines and TransversalsConcept Practice
2 marks~3 minCriterion A
The diagram shows two parallel lines cut by a transversal (a line crossing both). One pair of corresponding angles is marked: one angle measures 75°75° and the other is unknown.
a
State the relationship between corresponding angles when two parallel lines are cut by a transversal. [1]
b
Calculate the unknown angle. [1]
Question diagram

Solutions

12QuestionProperties of Isosceles Equilateral and Right TrianglesAssessment Practice
6 marks~9 minCriterion C
In isosceles triangle ABCABC, AB=ACAB = AC and ∠BAC=40°\angle BAC = 40°. Point DD lies on BCBC such that AD=ABAD = AB.
a
State the size of ∠ABC\angle ABC. [1]
b
Calculate the size of ∠BAD\angle BAD, showing your working. [2]
c
Triangle ABDABD has two equal sides. Explain what this tells you about ∠BAD\angle BAD and ∠BAC\angle BAC, and what this reveals about point DD. [3]
Question diagram

Solutions

13QuestionProperties of Squares Rectangles Parallelograms and TrapeziumsAssessment Practice
5 marks~8 minCriterion D
A carpenter builds a rectangular table frame with sides of 120 cm and 90 cm. When measured, the two diagonals are 152 cm and 149 cm.
a
State the property of rectangles that relates to their diagonals. [1]
b
Calculate the expected diagonal length of a perfect rectangle with sides 120 cm and 90 cm. [2]
c
Compare the measured diagonals with your calculated value and decide whether the frame is a perfect rectangle. Include one reason why the measurements might differ from the expected value. [2]
Question diagram

Solutions

14QuestionTessellating Shapes and PatternsAssessment Practice
8 marks~12 minCriterion B
A student claims: "Any regular polygon can tessellate because they are all symmetrical."

A regular pentagon has an interior angle of 108°108°. The diagram shows three pentagons meeting at a point, leaving a gap.

Tessellation: a pattern of shapes that covers a surface with no gaps or overlaps.
a
Calculate the total angle where three pentagons meet at a point. [2]
b
Explain why regular pentagons cannot tessellate. Use your answer to part (a) and the fact that angles around a point must sum to 360°360°. [2]
c
A regular hexagon has an interior angle of 120°120°. A regular octagon has an interior angle of 135°135°. Compare these two polygons and determine which one can tessellate. Show your working for both. [4]
Question diagram

Solutions

15QuestionCreating Symmetrical DesignsAssessment Practice
7 marks~11 minCriterion D
A graphic designer is creating a wallpaper for a curved museum wall. The wall has an area of 45 m². The design uses a tessellation of identical quadrilateral tiles, each with an area of 0.09 m². The designer treats the wall as perfectly flat.
a
Calculate the number of tiles needed for the wall. [2]
b
Explain two reasons why a flat tessellation pattern may not work well on a curved wall. [3]
c
Compare using large tiles versus small tiles on a curved wall, and state which is better suited. [2]
Question diagram

Solutions

16QuestionIdentifying Line Symmetry in ShapesAssessment Practice
4 marks~6 minCriterion C
The four irregular hexagons below each show a drawn line of symmetry.
a
Identify which two hexagons (A, B, C, or D) have a valid line of symmetry. [1]
b
For each valid hexagon you identified, explain how you know the line is a true line of symmetry. [2]
c
Compare the two invalid lines of symmetry. Explain what both drawn lines have in common that makes them fail. [1]
Question diagram

Solutions

17QuestionTesting 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]
Question diagram

Solutions

18QuestionExploring 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]
Question diagram

Solutions

19QuestionExploring Tangents and Secants IntroductoryAssessment Practice
6 marks~9 minCriterion B
A tangent and a secant meet at a point on a circle. The table shows the intercepted arc (the arc cut off between the two points where the secant crosses the circle) and the angle between the tangent and secant.

Intercepted arc: 60°, 90°, 120°, 150°60°,\ 90°,\ 120°,\ 150°
Angle: 30°, 45°, 60°, 75°30°,\ 45°,\ 60°,\ 75°
a
State the relationship between the angle and the intercepted arc. [1]
b
Explain how you would find the angle when the intercepted arc is 160°160°. Show your working. [2]
c
A classmate says: "The angle equals the intercepted arc because both come from the same arc." Compare this claim with the inscribed angle theorem (an inscribed angle equals half its intercepted arc) and explain whether your classmate is correct. [3]
Question diagram

Solutions

20QuestionSymmetry and Angle Properties in CirclesAssessment Practice
3 marks~5 minCriterion C
In the diagram, OO is the centre of a circle. Points AA, BB, and CC lie on the circumference. Angle AOB=80°AOB = 80°.
a
Identify the type of angle that ∠ACB\angle ACB is. [1]
b
Calculate the measure of ∠ACB\angle ACB. [1]
c
A classmate says: "If CC were moved to a different position on the same arc, ∠ACB\angle ACB would change." Explain whether your classmate is correct. [1]
Question diagram

Solutions

21QuestionUnderstanding Central Angle and CircumferenceAssessment Practice
6 marks~9 minCriterion D
A sports centre is designing a circular running track with a radius of 50 m. A sector (a "pizza-slice" region) is marked with a central angle of 72°. Use π=3.14\pi = 3.14.
a
Calculate the arc length of the sector. [2]
b
Explain why the formula Arc Length=angle360×2πr\text{Arc Length} = \dfrac{\text{angle}}{360} \times 2\pi r only works when the angle is measured in degrees. [2]
c
State one limitation of using this formula to design a real running track, and explain how it could affect the build. [2]
Question diagram

Solutions

22QuestionAngle Sum in a Triangle and QuadrilateralAssessment Practice
4 marks~6 minCriterion D
A park ranger measures the three angles of a triangular plot of land as 58°58°, 62°62°, and 60°60°. Each measurement has a possible error of ±1°\pm 1°.
a
State the measured sum of the three angles. [1]
b
Calculate the minimum possible sum and the maximum possible sum of the angles, accounting for the measurement error. [2]
c
Explain why the ranger's claim that the map is accurate cannot be fully trusted, and identify one limitation of using only the angle sum rule to check a triangle's accuracy. [1]
Question diagram

Solutions

23QuestionAngles on a Straight Line and Around a PointAssessment Practice
4 marks~6 minCriterion D
A carpentry student measures two angles formed where two wooden planks meet along a straight edge. The recorded angles are 73°73° and 107°107°. The protractor used has a margin of error (the range within which the true value may lie) of ±1°\pm 1°.
a
Calculate the sum of the two measured angles. [1]
b
The student claims the angles are supplementary (summing to exactly 180°180°). Using the margin of error, identify the smallest and largest possible sums, and explain whether the student's claim is fully valid. [2]
c
Describe one limitation of using only a protractor to check that a carpentry joint is straight. [1]
Question diagram

Solutions

24QuestionAngle Relationships in Parallel Lines and TransversalsAssessment Practice
5 marks~8 minCriterion C
Two parallel lines are cut by a transversal, forming the angles shown in the diagram.

Angle A=50°A = 50°, Angle B=130°B = 130°, Angle C=xC = x.
a
Identify the relationship between Angle AA and Angle BB. [1]
b
Calculate the value of xx, showing the angle relationship you used. [3]
c
A classmate says xx could equal 130°130° instead. Explain why they are incorrect. [1]
Question diagram

Solutions