Are these practice questions for A Tale of Three Intersecting Lines based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 7 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for A Tale of Three Intersecting Lines free?

Yes. Every chapter includes free practice questions for Class 7 students to get you started.

What types of questions are included?

The practice set for A Tale of Three Intersecting Lines mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for A Tale of Three Intersecting Lines for full coverage.

How many practice questions are there for A Tale of Three Intersecting Lines?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

A Tale of Three Intersecting Lines Class 7 Mathematics Practice Questions with Answers

easy

Examine if a triangle can be formed with side lengths of

6

cm,

9

cm, and

16

cm. Justify your answer.

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easy

Describe the Angle Sum Property of a triangle.

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easy

The three angles of a triangle are in the ratio

1:2:3

. Calculate the measure of each angle and classify the triangle based on its angles.

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easy

Explain why it is more efficient to use a compass and a ruler to construct an equilateral triangle than just a ruler.

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easy

Create a set of three side lengths that would form an isosceles triangle but not an equilateral triangle. Justify that your chosen lengths can indeed form a triangle by using the triangle inequality theorem.

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easy

Design a set of measurements (two angles and an included side) for which it is impossible to construct a triangle. Justify why your chosen values make the construction impossible.

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easy

Define an equilateral triangle.

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easy

Critique the following statement and justify your conclusion: 'It is possible to construct an equilateral triangle that is also an obtuse-angled triangle.'

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easy

In

\triangle ABC

, if

\angle A = 55^\circ

and

\angle B = 45^\circ

, calculate the measure of

\angle C

.

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easy

Name the three types of triangles based on the lengths of their sides.

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easy

What is the sum of the three angles in any triangle?

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medium

In an isosceles triangle, the vertex angle is

80^\circ

. An exterior angle is formed by extending the base at one of the vertices. Calculate the measure of this exterior angle.

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medium

Rohan claims he has constructed a triangle with angles

40^\circ

,

60^\circ

, and

80^\circ

. Anjali also claims she has constructed a triangle with the same angles, but her triangle is visibly larger than Rohan's. Critique this situation and justify whether it is possible for both of them to be correct.

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medium

Consider an isosceles triangle

\triangle ABC

where

AB = AC

. (a) If the vertex angle

\angle A = 40^\circ

, calculate the measure of the base angles

\angle B

and

\angle C

. (b) The side

BC

is extended to a point

D

. Calculate the exterior angle

\angle ACD

. (c) Using your results, demonstrate that the exterior angle

\angle ACD

is equal to the sum of the interior opposite angles.

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medium

Justify why, when checking the triangle inequality for sides

a, b, c

, it is sufficient to only check if the sum of the two shorter sides is greater than the longest side.

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medium

Create a formal proof, complete with a labeled diagram, to demonstrate that the sum of the interior angles of any triangle is always

180^\circ

. Justify your steps using the properties of parallel lines and transversals.

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medium

Describe the complete process for constructing a triangle when the lengths of its three sides are given, for example, 5 cm, 6 cm, and 7 cm. List the tools required and explain the role of each step.

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medium

In

\triangle XYZ

, the measure of

\angle X

is

30^\circ

more than

\angle Y

, and

\angle Z

is a right angle. Calculate the measures of

\angle X

and

\angle Y

.

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medium

Explain what happens if you try to construct a triangle with side lengths 4 cm, 5 cm, and 10 cm. Relate this to the triangle inequality.

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medium

Propose a logical reason, based on the angle sum property, why the sum of any two angles in a triangle must always be less than

180^\circ

.

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medium

Identify the property that must be satisfied by the side lengths for a triangle to be possible.

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medium

Describe the difference between an acute-angled triangle, a right-angled triangle, and an obtuse-angled triangle.

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medium

Evaluate the statement: 'If you are given the lengths of three sides that satisfy the triangle inequality, you can construct only one unique triangle.' Justify your answer.

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medium

Analyze why a triangle cannot have two obtuse angles.

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medium

In an isosceles triangle, one of the equal base angles is

50^\circ

. Calculate the vertex angle.

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medium

A student attempts to construct a triangle with side lengths

4

cm,

6

cm, and

11

cm. They draw the

11

cm base, then use a compass to draw arcs from each endpoint. Justify geometrically why the two arcs will never intersect.

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medium

Summarize the Triangle Inequality property. Explain with an example how to use this property to check if a triangle can be formed with side lengths 12 cm, 7 cm, and 4 cm.

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medium

Two sides of a triangular garden measure

10

m and

15

m. Analyze and determine the possible range of lengths for the third side.

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medium

Summarize the steps to construct a triangle when two sides and the included angle are given.

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medium

List the three cases of given measurements for which the construction of a unique triangle is described in the text.

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medium

An exterior angle of a triangle is

125^\circ

. If one of the interior opposite angles is

70^\circ

, calculate the other interior opposite angle.

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medium

A plot of land is shaped like a triangle

\triangle PQR

. Solve the following problems related to it. (a) The owner claims the side lengths are

PQ = 45

m,

QR = 105

m, and

RP = 58

m. Analyze if a triangular plot with these dimensions is possible. (b) In a different valid triangular plot, the angle at vertex

P

is

80^\circ

and the angle at vertex

Q

is

42^\circ

. Calculate the angle at vertex

R

. (c) In a third plot, the side

QR

is extended to a point

S

. If

\angle P = 60^\circ

and

\angle Q = 50^\circ

, calculate the exterior angle

\angle PRS

.

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medium

What is an altitude of a triangle?

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medium

Evaluate whether it is possible for a triangle to be both right-angled and isosceles. If it is possible, design the measures for its three angles and justify your design using the angle sum property.

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medium

A triangle has side lengths of

7

cm,

7

cm, and

10

cm. Examine if this triangle is possible and, if so, classify it based on its sides.

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medium

Formulate a logical argument to prove that the exterior angle of a triangle is equal to the sum of its two interior opposite angles. You may use the fact that the sum of angles in a triangle is

180^\circ

.

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hard

Formulate a general rule, in the form of a compound inequality, for the possible length of the third side of a triangle,

c

, given the lengths of the other two sides,

a

and

b

.

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hard

A designer is creating a logo based on a triangle

\triangle XYZ

. Solve the following design problems. (a) The first proposal has side lengths

8

cm,

15

cm, and

6

cm. Analyze if a triangle can be constructed with these side lengths and provide a reason. (b) In a second design, the triangle is an isosceles right-angled triangle with

\angle X = 90^\circ

and side

XY = XZ

. Calculate the measures of angles

\angle Y

and

\angle Z

. (c) In a third design, the exterior angle at vertex

Z

is

140^\circ

, and the interior angle

\angle Y = 85^\circ

. Calculate the interior angle

\angle X

.

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hard

Explain the condition related to the sum of two angles for a triangle to be possible when two angles and an included side are given.

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hard

Explain how the concept of parallel lines is used to prove that the sum of the angles in a triangle is

180^\circ

. You can describe the steps with reference to a general triangle

\triangle ABC

.

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hard

In

\triangle ABC

, a line segment

DE

is drawn with

D

on side

AB

and

E

on side

AC

, such that

DE

is parallel to

BC

. If

\angle ABC = 55^\circ

and

\angle ACB = 45^\circ

, calculate all three angles of

\triangle ADE

.

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hard

Design a step-by-step geometric construction method using a compass and a straightedge to find the altitude from vertex P for an obtuse-angled triangle

\triangle PQR

where

\angle Q

is the obtuse angle. Justify why your method works, explaining how it ensures the constructed line is perpendicular to the line containing side

\overline{QR}

.

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hard

A student correctly constructs a triangle with side lengths

6

cm,

8

cm, and

10

cm and observes that it appears to be a right-angled triangle. Critique this observation and justify mathematically why this specific set of side lengths must form a right-angled triangle.

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hard

An architect is designing a triangular garden plot with two sides measuring

8

m and

13

m. Formulate a compound inequality that describes all possible lengths,

x

, for the third side. Justify why a side length of

4

m is impossible, and then propose two different valid lengths for the third side that would make the garden an isosceles triangle.

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hard

One angle of a triangle is equal to the sum of the other two angles. Calculate the measure of this specific angle and demonstrate what type of triangle it is.

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A Tale of Three Intersecting LinesClass 7 Mathematics Practice Questions