**Hint:** Measure the given line segments in order to compare them.

**Question.1.** Consider the figures below.Which option correctly represents the lengths of two pencils, A and B?

(a) Pencil A = Pencil B = 7 cm

(b) Pencil A = Pencil B = 8 cm

(c) Pencil A = 9 cm, Pencil B = 8 cm

(d) Pencil A = 11 cm, Pencil B = 9 cm

**Question.2.** Consider the image below.Which of these options correctly compares the lengths of objects?

(a) Nail > Straw > Paper Clip > Safety pin

(b) Paper clip < Safety pin < Straw < Nail

(c) Nail > Safety pin > Paper clip > Straw

(d) Nail < Safety pin < Paper clip < Straw

**Ans.1.** (a) Pencil A = Pencil B = 7 cm**Ans.2.** (d) Nail < Safety pin < Paper clip < Straw

**Hint:** Examine the rotation of angles in order to classify angles based on the amount of rotation.

**Question.3.** Which of these will result a straight angle?

(a) Turn from East to North by a right angle

(b) Turn from South to East by three right angles

(c) Turn from North to South by two right angles

(d) Turn from West to South by three right angles

**Question.4.** Consider the statements.**Statement 1:** Taking a turn from South to North by two right angles will form a straight angle.**Statement 2:** Taking a turn from West to South by three right angles will form a reflex angle.

Which of these statement(s) is/are correct?

(a) Only Statement 1

(b) Only Statement 2

(c) Both Statement 1 and Statement 2

(d) Neither Statement 1 nor Statement 2

**Ans.3.** (c) Turn from North to South by two right angles**Ans.4.** (c) Both Statement 1 and Statement 2

**Hint:** Compare the given angles in order to classify them as a right angle, straight angle or a complete angle.

**Question.5.** Consider the angles shown.Which option correctly classifies the given angles?

(a) There are 3 right angles, 2 straight angles and 1 complete angle

(b) There are 2 right angles, 3 straight angles and 1 complete angle

(c) There are 3 right angles, 1 straight angle and 2 complete angles

(d) There are 2 right angles, 1 straight angle and 2 complete angles

**Question.6.** Consider the angles shown.Which table correctly classifies the angles?

(a) (b) (c) (d)

**Ans.5.** (b) There are 2 right angles, 3 straight angles and 1 complete angle**Ans.6.** (a)

**Hint:** Compare the given angles in order to classify them as an acute angle, obtuse angle or a reflex angle according to their measure.

**Question.7.** Consider the image below.Classify the angles as acute and obtuse angles.

(a) (b) (c) (d)

**Question.8.** The figure shows 8 rays having a common vertex X.Which options correctly shows the number of acute, obtuse and reflex angles formed by different rays?

(a) (b) (c) (d)

**Ans.7.** (c) **Ans.8.** (b)

**Hint:** Identify the different types of angles in our surroundings in order to demonstrate an understanding of angles.

**Question.9.** Consider the angles marked in the figures below.Which option correctly classifies the angles marked?

(a) (b) (c) (d)

**Question.10.** A ladder is placed against a wall as shown below.If the feet of the ladder are pulled towards east such that they remain on the ground only, which statement best describes the effect on inside angle between the wall and the ladder?

(a) The inside angle between the wall and the ladder will still be an acute angle.

(b) The inside angle between the wall and the ladder will still be an obtuse angle.

(c) The inside angle between the wall and the ladder will change from obtuse to a right angle.

(d) The inside angle between the wall and the ladder will change from acute to an obtuse angle.

**Ans.9.** (b) **Ans.10.** (a) The inside angle between the wall and the ladder will still be an acute angle.

**Hint:** Use a protractor in order to measure the given angle and classify its type.

**Question.11.** Aniket has to measure and classify \angleCOD shown below.He places the protractor to measure the angle as shown.Which option correctly represents the measurement and type of \angleCOD?

(a) \angleCOD = 125°; Obtuse angle

(b) \angleCOD = 125°; Acute angle

(c) \angleCOD = 55°; Obtuse angle

(d) \angleCOD = 55°; Acute angle

**Question.12.** A teacher asks his students to measure \angleBAC, \angleBAD and \angleBAE also classify their types.One of the students places the protractor as shown below.Based on the measurements, the student writes the answer as

\angleBAC = 45°; Obtuse angle

\angleBAD = 90°; Right angle

and \angleBAE = 120°; Acute angle. Which is true about the student’s answer?

(a) The student measures the angles correctly as the mid-point of the protractor lies at the common initial point (vertex), A, and also classifies the angles correctly as obtuse angle < 90°, right angle = 90° and 90°< acute angle < 180°.

(b) The student measures the angles correctly as the mid-point of the protractor lies at the common initial point (vertex), A, but classifies the angles incorrectly as acute angle < 90°, and 90°< obtuse angle < 180°.

(c) The student measures the angles incorrectly as the mid-point of the protractor must lie at B, but the classification would still be the same with the correct angle’s measures.

(d) The student measures the angles incorrectly as the mid-point of the protractor must lie at B and the classification will change for the correct angle’s measures.

**Ans.11.** (d) \angleCOD = 55°; Acute angle**Ans.12.** (b) The student measures the angles correctly as the mid-point of the protractor lies at the common initial point (vertex), A, but classifies the angles incorrectly as acute angle < 90°, and 90°< obtuse angle < 180°.

**Hint:** Use a protractor in order to draw an angle of the given measure.

**Question.13.** Jignesh is drawing an angle of measure 80°. His part of work is shown below.Which of the following shows the complete drawing?

(a) (b) (c) (d)

**Question.14.** A teacher asks his students if it is possible to draw an angle PQR of measure 60° given the locations of points P and Q as shown.Which option shows the correct response to the teacher’s question?

(a) Yes, there is one possibility to draw the required angle.

(b) Yes, there are two possibilities to draw the required angle.

(c) No, but relocating the point P to a different location can lead one possibility to draw the required angle.

(d) No, but relocating the point P to a different location can lead two possibilities to draw the required angle.

**Ans.13.** (b) **Ans.14.** (b) Yes, there are two possibilities to draw the required angle.

**Hint:** Describe perpendicular and a perpendicular bisector in order to identify the same in the given figure.

**Question.15.** Consider the image below.If line u is perpendicular to line v, which statement is correct?

(a) Line u is perpendicular to \overline{JS}; \overline{JS} bisects \overline{HL}.

(b) Line u is perpendicular to \overline{JS}; \overline{JS} bisects \overline{FM}.

(c) Line v is perpendicular to \overline{FM}; \overline{JS} bisects \overline{HK}.

(d) Line v is perpendicular to \overline{FM}; \overline{JS} bisects \overline{FK}.

**Question.16.** Anish draws a figure as shown.He says that \overline{UT} is the perpendicular bisector of \overline{GH}.

Which condition is sufficient to justify his claim?**Condition A:** \overline{HK}⊥ \overline{UT}**Condition B:** \overline{GH} = 2 \overline{GK}

(a) Both conditions together are sufficient, but neither condition alone is sufficient

(b) Condition 2 alone is sufficient, but condition 1 alone is not sufficient

(c) Condition 1 alone is sufficient, but condition 2 alone is not sufficient

(d) Conditions 1 and 2 together are not sufficient

**Ans.15.** (a) Line u is perpendicular to \overline{JS}; \overline{JS} bisects \overline{HL}.**Ans.16.** (a) Both conditions together are sufficient, but neither condition alone is sufficient

**Hint:** Give example(s) of perpendicular lines in order to demonstrate an understanding of the same.

**Question.17.** Consider the alphabets below.How many alphabets have at least one perpendicular line?

(a) One

(b) Two

(c) Three

(d) Four

**Question.18.** Some books are placed on a wooden shelf as shown.How many books are perpendicular to the wooden shelf?

(a) 1

(b) 2

(c) 7

(d) 9

**Ans.17.** (d) Four**Ans.18.** (c) 7

**Hint:** Observe the measure of sides of a triangle in order to classify it into different types (scalene, isosceles, equilateral) based on its sides.

**Question.19.** Three triangles, Triangle 1, Triangle 2 and Triangle 3, have their sides marked as AB, BC and AC. Which table correctly classifies the triangles?

(a) (b) (c) (d)

**Question.20.** Consider the table.Which option correctly completes the table?

(a) (b) (c) (d)

**Ans.19.** (a) **Ans.20.** (b)

**Hint:** Observe the measure of angles of a triangle in order to classify it into different types (acute, obtuse, right) based on its angles.

**Question.21.** Consider the triangles below.Which table correctly classifies the triangles with correct justification?

(a) (b) (c) (d)

**Question.22.** A question in a mathematics book requires making different types of triangles using 8 vertices, A, B, C, D, E, F, G and H such that A and B must be the vertices of every triangle.How many different types of triangles can be formed to correctly answer the question?

(a) (b) (c) (d)

**Ans.21.** (a) **Ans.22.** (a)

**Hint:** Examine the given figures in order to classify type quadrilaterals based on their properties.

**Question.23.** Consider the quadrilaterals shown.Which option correctly classifies the quadrilaterals?

(a) (b) (c) (d)

**Question.24.** Three quadrilaterals are formed by joining triangles.

**Quadrilateral A:**By joining two identical right-angled isosceles triangles at their hypotenuse.**Quadrilateral B:**By joining two identical scalene right-angled triangles at their hypotenuse.**Quadrilateral C:**By joining two identical equilateral triangles at a common side.

Which option correctly classifies the quadrilaterals based on their properties?

(a) (b) (c) (d)

**Ans.23.** (b) **Ans.24.** (c)

**Hint:** Examine the given figures in order to identify polygons.

**Question.25.** Consider the polygon shown.Lubna says that the given polygon is a heptagon. Is she correct?

(a) No, because a heptagon is made of6 line segments.

(b) Yes, because a heptagon is made of 7 line segments.

(c) No, because a heptagon must have exactly3 reflex angles.

(d) Yes, because a heptagon must have exactly 2 reflex angles.

**Question.26.** Consider the figures.Which of these figure(s) can be classified as polygon(s)?

(a) Figure 3; as it is not made of line segments.

(b) Figures 2 and 5; as these are not closed figures.

(c) Figures 1, 4 and 6; as these are closed figures made of line segments.

(d) All 6 figures as these are flat shapes.

**Ans.25.** (b) Yes, because a heptagon is made of 7 line segments.**Ans.26.** (c) Figures 1, 4 and 6; as these are closed figures made of line segments.

**Hint:** Describe polygons in order to classify them based on their number of sides and angles. (Up to 8 sides)

**Question.27.** Observe the polygons shown.Which table correctly classifies the given polygons?

(a) (b) (c) (d)

**Question.28.** A task in a quiz requires making different types of polygons using 8 vertices, A, B, C, D, E, F and G such that A, B and C must be the vertices of every polygon. A student joins C to A and A to B as shown.How many different types of polygons can the student form to correctly complete the task?

(a) 1

(b) 4

(c) 5

(d) 8

**Ans.27.** (c) **Ans.28.** (b) 4

**Hint:** Give example(s) in order to distinguish between regular and irregular polygons.

**Question.29.** Which of the following correctly differentiates the given polygons as regular and irregular?

(a) (b) (c) (d)

**Question.30.** Consider the table shown.Is the table correctly distinguishing between regular and irregular polygons?

(a) Yes, because polygons with equal sides and equal angles are classified as regular polygons, whereas irregular polygons do not have all sides equal and all angles equal.

(b) No, because polygons with equal sides and equal angles are classified as irregular polygons, whereas regular polygons do not have all sides equal and all angles equal.

(c) Yes, because polygons with equal opposite sides are classified as regular polygons, whereas irregular polygons do not have equal opposite sides.

(d) No, because polygons with equal opposite sides are classified as irregular polygons, whereas regular polygons do not have equal opposite sides.

**Ans.29.** (d) **Ans.30.** (a) Yes, because polygons with equal sides and equal angles are classified as regular polygons, whereas irregular polygons do not have all sides equal and all angles equal.

**Hint:** Describe solid shapes in order to distinguish them from flat shapes.

**Question.31.** Rahul and Avantika draw two shapes. Rahul draws a shape with four sides and four corners and Avantika draws a shape with 6 faces such that each face has four corners. Who among them has/have drawn a solid shape?

(a) Only Rahul

(b) Only Avantika

(c) Both Rahul and Avantika

(d) Neither Rahul nor Avantika

**Question.32.** A teacher describes the properties of some shapes in the table shown and asks his students to correctly classify the shapes as flat or solid.Which option correctly classifies the shapes?

(a) (b) (c) (d)

**Ans.31.** (b) Only Avantika**Ans.32.** (a)

**Hint:** Examine the given solid shapes in order to identify their type (Cubes, Cuboids, cylinder, sphere, cone, prism, pyramid)

**Question.33.** A teacher draws two shapes and asks her students to identify the shapes.The responses of two of the students are as**Student 1:** Figure P is a pyramid.**Student 2:** Figure Q is a prism.

Who is/are correct?

(a) Only Student 1

(b) Only Student 2

(c) Both Student 1 and Student 2

(d) Neither Student 1 nor Student 2

**Question.34.** Ananya places two identical cubes one over the other. What would be the shape of the resultant solid?

(a) Cube

(b) Cuboid

(c) Triangular Pyramid

(d) Rectangular pyramid

**Ans.33.** (c) Both Student 1 and Student 2**Ans.34.** (b) Cuboid

**Hint:** Describe the faces, edges and vertices of a 3D shape in order to discuss the various aspects of the given 3D object

**Question.35.** Which of these tables correctly represents the number of faces, vertices and edges in triangular pyramid and cuboid?

(a) (b) (c) (d)

**Question.36.** Simran places a square pyramid at the top of a cube. How many faces, edges and vertices does the resulting shape have?

(a) Faces = 9, Edges = 16 and Vertices = 9

(b) Faces = 16, Edges = 9 and Vertices = 9

(c) Faces = 10, Edges = 16 and Vertices = 9

(d) Faces = 9, Edges = 16 and Vertices = 10

**Ans.35.** (d) **Ans.36.** (a) Faces = 9, Edges = 16 and Vertices = 9