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Geometry – Properties of Shape — Free MYP1 Mathematics Practice Questions
1QuestionClassifying Triangles by Sides and AnglesConcept Practice
2 marks~3 minCriterion A
A triangle has side lengths of cm, cm, and cm.
a
Name the type of triangle. [1]
b
Describe the property that makes it this type of triangle. [1]
Solutions
2QuestionSum of Interior and Exterior Angles in PolygonsConcept Practice
4 marks~6 minCriterion B
The diagram shows a regular pentagon with all five interior angles labelled.
a
Name the number of sides a pentagon has. [1]
b
Describe, in one sentence, how to find the sum of the interior angles of any polygon. [1]
c
State the name of a different polygon and calculate the sum of its interior angles. [2]
Solutions
3QuestionProperties of Isosceles Equilateral and Right TrianglesConcept Practice
4 marks~6 minCriterion C
The diagram shows isosceles triangle , where is at the top and and are at the bottom.
a
Identify the two sides of triangle that are equal in length. [1]
b
Describe what is true about the two angles at and . [1]
c
Describe how a yield (give-way) road sign and the triangular face of a tent are both similar to, and different from, an isosceles triangle. [2]
Solutions
4QuestionCreating Symmetrical DesignsConcept Practice
2 marks~3 minCriterion D
The McDonald's logo has a large letter "M" made of two golden arches.
a
Name the type of symmetry shown in the McDonald's "M" logo. [1]
b
Describe how this symmetry makes the logo easy to recognise. [1]
Solutions
5QuestionTessellating Shapes and PatternsConcept Practice
2 marks~3 minCriterion A
A tessellation is a pattern made by repeating a shape to cover a flat surface.
a
State one word that describes what a tessellation must have between its shapes. [1]
b
Describe what this means in a full sentence. [1]
Solutions
6QuestionIdentifying Line Symmetry in ShapesConcept Practice
2 marks~3 minCriterion B
A regular polygon has the same number of lines of symmetry as it has sides.
| Shape | Sides | Lines of symmetry |
|---|---|---|
| Triangle | 3 | 3 |
| Square | 4 | 4 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 6 |
a
Identify the pattern shown in the table. [1]
b
State the number of lines of symmetry for a regular octagon. [1]
Solutions
7QuestionExploring 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
8QuestionExploring 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
9QuestionExploring 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
10QuestionExploring Tangents and Secants IntroductoryConcept Practice
4 marks~6 minCriterion C
The diagram shows a circle with centre O. A radius is drawn to point T on the circle. A tangent line touches the circle at point T.
a
Name the type of angle formed between the radius OT and the tangent line at point T. [1]
b
Describe what a tangent line does at the point where it meets a circle. [1]
c
The corner of a square and the angle between a radius and a tangent both measure . Describe one way they are the same and one way they are different. [2]
Solutions
11QuestionSymmetry and Angle Properties in CirclesConcept Practice
4 marks~6 minCriterion B
The diagram shows a circle with centre . A line segment is drawn from to the circumference, and a second line segment is drawn from to a different point on the circumference.
a
Name the type of line segment shown. [1]
b
Describe what a diameter is, using the word radius in your answer. [1]
c
Compare the two line segments drawn from centre to the circumference. Describe what is the same and what would happen if you drew more line segments like these in the same circle. [2]
Solutions
12QuestionDrawing Circles with Compass and RulerConcept Practice
3 marks~5 minCriterion A
A circle is drawn with centre . Point lies on the circumference. The distance cm.
a
Name the distance . [1]
b
Describe, in one sentence, how the diameter and the radius of a circle are related. [1]
c
Calculate the diameter of the circle. [1]
Solutions
13QuestionNaming Parts of a Circle Radius Diameter Chord ArcConcept Practice
4 marks~6 minCriterion D
A circular fountain in a park has a radius of 3 m.
a
Name the formula that links radius and diameter. [1]
b
Calculate the expected diameter of the fountain. [1]
c
A worker measures the actual diameter as 5 m. Describe one difference between the expected diameter and the actual diameter. [2]
Solutions
14QuestionUsing Geometric Reasoning to Find Missing AnglesConcept Practice
2 marks~3 minCriterion D
A map shows three islands forming a triangle. Two of the angles are and .
a
Calculate the missing angle of the triangle. [1]
b
Describe one reason why the angle you calculated might not give the captain an accurate heading in real life. [1]
Solutions
15QuestionSolving Problems with Justification and ProofConcept Practice
4 marks~6 minCriterion C
Two straight lines cross at a point, forming four angles labelled , , , and . Angle .
a
Identify the two pairs of vertically opposite angles in the diagram. [1]
b
Describe, in one sentence, how you can find the size of angle . [1]
c
Compare vertically opposite angles with angles on a straight line. State one way they are the same and one way they are different. [2]
Solutions
16QuestionAngle Sum in a Triangle and QuadrilateralConcept Practice
4 marks~6 minCriterion B
The diagram shows a triangle with a straight line passing through one vertex, lying flat along the top. The three angles along the straight line match the three interior angles of the triangle.
a
State the sum of the angles on a straight line. [1]
b
Describe what you notice about the angles along the straight line and the angles inside the triangle. [2]
c
Compare the angle sum on a straight line with the angle sum inside a triangle, and explain what this tells us. [1]
Solutions
17QuestionUsing Geometric Reasoning to Find Missing AnglesConcept Practice
2 marks~3 minCriterion A
A right angle is split into two smaller angles. One angle is and the other is .
a
State the size of a right angle. [1]
b
Calculate the value of . [1]
Solutions
18QuestionConstructing and Measuring Angles with ProtractorConcept Practice
3 marks~5 minCriterion A
Ray sits between rays and , splitting into two smaller angles. The measure of is and the measure of is .
a
Name the two smaller angles that together make up . [1]
b
Write a number sentence to show how and combine to give . [1]
c
Calculate the measure of . [1]
Solutions
19QuestionConstructing and Measuring Angles with ProtractorConcept Practice
2 marks~3 minCriterion D
A builder uses a protractor to check the angle of a ramp before it is opened to the public.
a
Identify a real-life situation where measuring an angle with a protractor is important. [1]
b
Describe why getting that angle measurement exactly right matters for safety or for the ramp to work properly. [1]
Solutions
20QuestionComplementary Supplementary and Vertical AnglesConcept Practice
4 marks~6 minCriterion A
A right angle is split into two smaller angles by a ray. One angle measures .
a
State the size of a right angle. [1]
b
Identify the name for two angles that add up to . [1]
c
Calculate the size of the other angle. Show your working. [2]
Solutions
21QuestionProperties of Squares Rectangles Parallelograms and TrapeziumsAssessment Practice
2 marks~3 minCriterion D
A gardener has a flower bed shaped like a trapezium. The two parallel sides measure 3 m and 5 m, and the height is 2 m.
Describe one reason why the calculated area might differ from the actual area of the flower bed. [2]
Describe one reason why the calculated area might differ from the actual area of the flower bed. [2]
Solutions
22QuestionUnderstanding Rotational SymmetryAssessment Practice
5 marks~8 minCriterion C
A regular pentagon has rotational symmetry of order 5.
a
Name the formula used to find the angle of rotation for a shape with rotational symmetry of order . [1]
b
Calculate the angle of rotation for the regular pentagon. Show your working. [2]
c
A student says: "A square turns onto itself more often than a regular pentagon as you spin it one full turn." State whether the student is correct and give one reason using the angles of rotation of both shapes. [2]
Solutions
23QuestionTesting 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
24QuestionConstructing and Measuring Angles with ProtractorAssessment Practice
5 marks~8 minCriterion B
The table below shows the number of sides of a shape and the total of its inside angles.
| Sides | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| Total of inside angles |
a
State how much the total of inside angles increases each time one more side is added. [1]
b
Describe the pattern you see between the number of sides and the total of inside angles. [2]
c
Calculate the total of inside angles for a shape with 12 sides. Show your working. [2]
Solutions