Grade 7 : Mathematics (Ganita Prakash) - 14. Constructions and Tilings (Set 5)

Question 1

An architect is designing a floor using only identical regular polygons of a single type meeting at every vertex without gaps or overlaps (a regular monohedral tiling).

Which of the following regular polygons can successfully form such a regular tiling?

Accepted Answer

C) Regular hexagons

Answer

A) Regular pentagons

Answer

B) Regular octagons

Answer

D) Regular decagons

Question 2

Assertion (A): A unique triangle can be constructed when the lengths of two sides are4 cmand9 cm, and the included angle is $55^\circ$.
Reason (R): According to the SAS (Side-Angle-Side) construction criterion, a triangle is uniquely determined if two sides and their included angle are given.

Select the correct statement:

Accepted Answer

A) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

B) Both (A) and (R) are true but (R) is not the correct explanation of (A).

Answer

C) (A) is true, but (R) is false.

Answer

D) (A) is false, but (R) is true.

Question 3

A student attempts to construct a triangle PQRusing ruler and compasses with given side measurements:$PQ = 7cm$, $QR = 3.5cm$, and $PR = 3.5cm$.

What will happen when the student draws arcs from points $Q$and$R$ to locate point $P$along the baseline?

Accepted Answer

D) The arcs touch at exactly one point on the segment, failing to form a triangle.

Answer

A) Two distinct intersecting points are found above and below the line.

Answer

B) An acute triangle is successfully constructed.

Answer

C) An obtuse triangle is successfully constructed.

Question 4

Consider a semiregular tiling around a single vertex made of regular octagons and squares.

How many regular octagons and squares must meet at each vertex to fill the complete $360^\circ$angle without gaps?

Accepted Answer

B) 2 octagons and 1 square

Answer

A) 1 octagon and 2 squares

Answer

C) 3 octagons and 1 square

Answer

D) 2 octagons and 2 squares

Question 5

Assertion (A): A triangle cannot be constructed with interior angle measures $45^\circ$, $65^\circ$, and $80^\circ$.
Reason (R): The sum of the interior angles of any triangle in a plane must be strictly equal to $180^\circ$.

Select the correct choice:

Accepted Answer

B) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

A) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

C) (A) is true, but (R) is false.

Answer

D) (A) is false, but (R) is true.

Question 6

A craftsman wants to make a tessellation using only regular pentagons. When he places three regular pentagons sharing a single vertex, a gap remains.

What is the measure of the angular gap left at this vertex?

Accepted Answer

D) $36^\circ$

Answer

A) $18^\circ$

Answer

B) $24^\circ$

Answer

C) $30^\circ$

Question 7

In the construction of a line parallel to line $m$passing through an external point$A$, a transversal ABintersects$m$ at $B$. Arcs are drawn to copy $\angle 1$at$B$ onto point $A$as$\angle 2$.

Which geometric property directly ensures that the new line is parallel to line $m$?

Accepted Answer

A) Alternate interior angles (or corresponding angles) are equal.

Answer

B) Co-interior angles are supplementary.

Answer

C) Vertically opposite angles are equal.

Answer

D) Adjacent supplementary angles add to $180^\circ$.

Question 8

A tiling pattern consists of regular triangles and regular hexagons. At each vertex, two hexagons and two equilateral triangles meet.

Does this configuration fill the vertex completely to form a valid tiling?

Accepted Answer

C) Yes, the sum of the angles is exactly $360^\circ$.

Answer

A) No, the sum is $300^\circ$, leaving a $60^\circ$gap.

Answer

B) No, the sum is$420^\circ$, causing an overlap.

Answer

D) No, regular hexagons can never tile with triangles.

Question 9

Assertion (A): It is impossible to construct a right-angled triangle with hypotenuse 10 cmand one leg11 cm.
Reason (R): In any right-angled triangle, the hypotenuse must be the longest side.

Choose the correct option:

Accepted Answer

B) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

A) (A) is false, but (R) is true.

Answer

C) Both (A) and (R) are true, but (R) is not the correct explanation of (A).

Answer

D) (A) is true, but (R) is false.

Question 10

A student is constructing an equilateral triangle of side 6 cm. She draws a base segment $BC = 6cm$and opens her compass to radius$r$. She then draws arcs centered at $B$and$C$ to intersect at $A$.

What must the radius $r$be set to on the compass?

Accepted Answer

C) 6 cm

Answer

A) 3 cm

Answer

B) 12 cm

Answer

D) Any radius strictly greater than 6 cm

Question 11

A floor pattern is being tested using regular 12-sided polygons (dodecagons) and equilateral triangles.

How many regular dodecagons and equilateral triangles must meet at each vertex to form a valid vertex configuration?

Accepted Answer

D) 2 dodecagons and 1 triangle

Answer

A) 1 dodecagon and 2 triangles

Answer

B) 1 dodecagon and 3 triangles

Answer

C) 3 dodecagons and 1 triangle

Question 12

Assertion (A): Giving only the three angles of a triangle ($60^\circ, 60^\circ, 60^\circ$) is sufficient to construct a unique triangle.
Reason (R): The AAA (Angle-Angle-Angle) condition produces infinitely many similar triangles of different sizes.

Choose the correct option:

Accepted Answer

A) (A) is false, but (R) is true.

Answer

B) Both (A) and (R) are true and (R) is the correct explanation.

Answer

C) Both (A) and (R) are true, but (R) is not the correct explanation.

Answer

D) (A) is true, but (R) is false.

Question 13

To bisect a given angle $\angle ABC$, an arc centered at $B$cuts the arms at$P$ and $Q$. Then, arcs of equal radius centered at $P$and$Q$ intersect at point $D$. Ray BDis drawn.

Which triangle congruence criterion proves that$ riangle BPD \cong riangle BQD$, confirming BDbisects$\angle ABC$?

Accepted Answer

B) SSS

Answer

A) SAS

Answer

C) RHS

Answer

D) ASA

Question 14

An artist wants to tile a wall using identical scalene triangles. None of the angles are equal and none of the sides are equal.

Can any general triangle tile the plane without leaving any gaps or overlaps?

Accepted Answer

C) Yes, because six such triangles can meet at a vertex with their angles summing to $2 	imes 180^\circ = 360^\circ$.

Answer

A) No, only equilateral and isosceles triangles can tile the plane.

Answer

B) No, because its interior angles are not divisors of $360^\circ$.

Answer

D) Only if the triangle has at least one right angle.

Question 15

During the construction of triangle XYZwhere$XY = 5cm$, $\angle X = 70^\circ$, and $\angle Y = 80^\circ$, a student wants to find $\angle Z$before drawing to double-check their work.

What is the measure of$\angle Z$?

Accepted Answer

A) $30^\circ$

Answer

B) $40^\circ$

Answer

C) $50^\circ$

Answer

D) $60^\circ$

Question 16

Assertion (A): Any arbitrary quadrilateral (even non-regular and irregular) can tile the plane.
Reason (R): The sum of the interior angles of any quadrilateral is always $360^\circ$.

Choose the correct option:

Accepted Answer

D) Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

A) (A) is true, but (R) is false.

Answer

B) (A) is false, but (R) is true.

Answer

C) Both (A) and (R) are true, but (R) is not the correct explanation of (A).

Question 17

To construct a perpendicular to line $L$through point$P$ lying on $L$, arcs are cut at points $A$and$B$ on $L$equidistant from$P$. Then, from $A$and$B$, arcs of radius $R$are drawn intersecting at$Q$.

What condition must radius $R$satisfy to ensure the arcs intersect?

Accepted Answer

B) $R > AP$

Answer

A) $R = AP$

Answer

C) $R < AP$

Answer

D) $R = \frac{1}{2}AP$

Question 18

A student is given three line segments:$a = 6cm$, $b = 8cm$, and $c = 15cm$.

Can these three line segments form a valid triangle?

Accepted Answer

C) No, because $6 + 8 < 15$, violating the triangle inequality theorem.

Answer

A) Yes, because all lengths are positive integers.

Answer

B) Yes, by the SSS construction criterion.

Answer

D) No, because $15 - 8 < 6$.

Question 19

Consider a regular tiling formed exclusively by equilateral triangles.

How many equilateral triangles meet at each vertex of this tiling?

Accepted Answer

A) 6

Answer

B) 5

Answer

C) 4

Answer

D) 3

Question 20

To construct a right-angled triangle ABCwith$\angle B = 90^\circ$, hypotenuse $AC = 13cm$, and leg $AB = 5cm$, what must be the calculated length of the other leg BC?

What is the length of BC?

Accepted Answer

C) 12 cm

Answer

A) 8 cm

Answer

B) 10 cm

Answer

D) 14 cm

Set 9Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Examination Instructions:

Discussion 0

Rating & Discussion Locked

Set 9Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Examination Instructions:

Discussion 0

Rating & Discussion Locked

Set 9Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Examination Instructions:

Share This Quiz

Discussion 0

Rating & Discussion Locked

More Quizzes for Grade 7

Grade 7 : Mathematics (Ganita Prakash) - Geometric Twins

Grade 7 : Mathematics (Ganita Prakash) - Large Numbers Around Us

Grade 7 : Science (Curiosity) - Electricity

Grade 7 : Mathematics (Ganita Prakash) - Working with Fractions

Grade 7 : Mathematics (Ganita Prakash) - Large Numbers Around Us

Grade 7 : Science (Curiosity) - Adolescence

Set 9Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Grade 7 : Mathematics (Ganita Prakash) - Constructions and Tilings

Examination Instructions:

Share This Quiz

Discussion 0

Rating & Discussion Locked

More Quizzes for Grade 7

Grade 7 : Mathematics (Ganita Prakash) - Geometric Twins

Grade 7 : Mathematics (Ganita Prakash) - Large Numbers Around Us

Grade 7 : Science (Curiosity) - Electricity

Grade 7 : Mathematics (Ganita Prakash) - Working with Fractions

Grade 7 : Mathematics (Ganita Prakash) - Large Numbers Around Us

Grade 7 : Science (Curiosity) - Adolescence