Are these practice questions for Triangles based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Triangles free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Triangles 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 Triangles for full coverage.

How many practice questions are there for Triangles?

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

Triangles Class 10 Mathematics Practice Questions with Answers

easy

Formulate a proof for the statement: If a line is drawn through the mid-point of one side of a triangle parallel to another side, it bisects the third side.

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easy

Propose a complete proof for the theorem stating that the ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.

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easy

Are all equilateral triangles similar? Explain your answer in one sentence.

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easy

Define similar figures.

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easy

In

\triangle PQR

, a line segment

ST

is drawn parallel to

QR

such that

S

is on

PQ

and

T

is on

PR

. If

PS = 4

cm,

SQ = 6

cm, and

PT = 5

cm, calculate the length of

TR

.

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easy

Let

ABCD

be a trapezium with

AB \| DC

. If the diagonals

AC

and

BD

intersect at point

O

, create a proof based on similarity to show that

\frac{AO}{OC} = \frac{BO}{OD}

.

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easy

In

\triangle ABC

,

\angle B = 75^\circ

and

\angle C = 50^\circ

. In

\triangle XYZ

,

\angle Y = 75^\circ

and

\angle Z = 50^\circ

. Examine if

\triangle ABC \sim \triangle XYZ

and state the criterion used.

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easy

In a triangle, a line segment is drawn parallel to one side, dividing the other two sides. If the segments of one side are

x

and

x-2

, and the corresponding segments of the other side are

x+2

and

x-1

, calculate the value of

x

.

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easy

State the Basic Proportionality Theorem, also known as Thales Theorem.

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medium

In

\triangle XYZ

, point

A

is on side

XY

and point

B

is on side

XZ

. If

XA = 3

cm,

AY = 5

cm,

XB = 4.5

cm and

BZ = 7.5

cm, determine if

AB \| YZ

.

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medium

In a right triangle

ABC

, right-angled at

B

, a perpendicular

BD

is drawn from

B

to the hypotenuse

AC

. Justify that

BD^2 = AD \cdot DC

.

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medium

State the converse of the Basic Proportionality Theorem and draw a diagram to illustrate it.

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medium

If two triangles

\triangle ABC \sim \triangle DEF

, what can you state about their corresponding angles and corresponding sides?

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medium

Given two equilateral triangles,

\triangle ABC

with a side length of 5 cm and

\triangle PQR

with a side length of 10 cm. Explain why these two triangles are similar, referring to the definition of similar polygons.

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medium

State and explain the SAS (Side-Angle-Side) similarity criterion for two triangles. Draw two triangles,

\triangle ABC

and

\triangle PQR

, that are similar by this criterion. Label the corresponding equal angles and the sides that are in proportion, and write the similarity in symbolic form.

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medium

Propose a formal proof for the theorem stating that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes.

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medium

The diagonals of a trapezium

PQRS

with

PQ \| SR

intersect at point

O

. If

PO = (3x - 1)

cm,

OR = (5x - 3)

cm,

QO = (2x + 1)

cm, and

OS = (6x - 5)

cm, solve for

x

.

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medium

Justify whether the Side-Side-Angle (SSA) condition is sufficient for the similarity of two triangles. If not, formulate a counterexample.

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medium

In

\triangle ABC

,

D

is the mid-point of

BC

. The angle bisectors of

\angle ADB

and

\angle ADC

meet

AB

and

AC

at

E

and

F

respectively. Formulate a proof to show that

EF \| BC

.

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medium

Describe the concept of a scale factor in the context of similar polygons. If quadrilateral ABCD is similar to quadrilateral PQRS and the ratio of corresponding sides

\frac{AB}{PQ} = \frac{2}{3}

, what does this scale factor tell you about the relative sizes of the two figures? What would be the ratio of their perimeters?

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medium

Describe the SSS (Side-Side-Side) similarity criterion. If

\triangle LMN \sim \triangle XYZ

by SSS similarity, write the relationship between their corresponding sides.

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medium

Design a proof to show that the line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.

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medium

In

\triangle PQR

,

PQ = 5

cm,

PR = 10

cm, and

\angle P = 50^\circ

. In

\triangle STU

,

ST = 7.5

cm,

SU = 15

cm, and

\angle S = 50^\circ

. Examine if the two triangles are similar.

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medium

A lamp post is 4.5 m high. A girl of height 1.5 m stands at a distance of 6 m from the base of the lamp post. Calculate the length of her shadow cast on the ground.

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medium

Explain the difference between congruent figures and similar figures. Provide one example of a pair of congruent figures and one example of a pair of similar figures.

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medium

In the given figure,

LM \| CB

and

LN \| CD

. If

AM = 4

cm,

MB = 6

cm, and

AN = 5

cm, calculate the length of

AD

.

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medium

Critique the following statement: 'If the corresponding altitudes of two triangles are proportional, the triangles must be similar.' Justify your reasoning.

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medium

In

\triangle ABC

, altitudes

AD

and

CE

intersect at point

P

. Formulate a proof to show that

PA \cdot PD = PC \cdot PE

.

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medium

List the three criteria for the similarity of two triangles.

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medium

The sides of

\triangle LMN

are 6 cm, 8 cm, and 10 cm. The sides of

\triangle DEF

are 9 cm, 12 cm, and 15 cm. Analyze if the triangles are similar. If yes, write the similarity relation in correct correspondence.

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hard

Propose a method, based on triangle similarity, to determine the height of a tall object (like a flagpole) using only a mirror and a measuring tape.

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hard

In

\triangle PQR

, right-angled at

Q

, an altitude

QS

is drawn to the hypotenuse

PR

. If

PS = 4

cm and

SR = 9

cm, calculate the length of the altitude

QS

.

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hard

In the figure,

\triangle ABE \cong \triangle ACD

. Analyze the relationship between

\triangle ADE

and

\triangle ABC

and demonstrate that they are similar.

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hard

Explain the relationship between congruent figures and similar figures. Are all congruent figures similar? Are all similar figures congruent? Justify your answers with a detailed explanation and provide examples using circles and squares.

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hard

In an equilateral triangle

ABC

,

D

is a point on side

BC

such that

BD = \frac{1}{3}BC

. Justify that

9AD^2 = 7AB^2

.

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hard

Explain the AA (Angle-Angle) similarity criterion. Why is it sufficient to show that only two pairs of corresponding angles are equal for two triangles to be similar?

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hard

Using the principles of similar triangles, create a proof for the Pythagoras Theorem.

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hard

Summarize the two conditions required for any two polygons with the same number of sides to be similar. Provide one example of a pair of quadrilaterals where corresponding angles are equal but they are not similar, and another example where corresponding sides are in the same ratio but they are not similar.

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hard

Two poles of height

a

meters and

b

meters are

p

meters apart. Prove that the height (

h

) of the intersection point of the lines joining the top of each pole to the foot of the opposite pole is given by

h = \frac{ab}{a+b}

meters.

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hard

Identify if a square with a side length of 4 cm and a rectangle with a length of 5 cm and a breadth of 4 cm are similar. Explain your reasoning based on the conditions for similarity of polygons.

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hard

A circle is drawn with side

BC

of

\triangle ABC

as its diameter. The circle intersects sides

AB

and

AC

at points

D

and

E

respectively. Devise a proof to show that

\triangle ADE \sim \triangle ABC

.

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TrianglesClass 10 Mathematics Practice Questions