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Chapter 6 · Class X Mathematics · MCQ Practice

MCQ Practice Arena

Triangles

Similarity, Proportionality, Pythagoras — Three Tools, Every Problem Solved

📋 50 MCQs ⭐ 28 PYQs ⏱ 85 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

15Easy

22Medium

13Hard

28PYQs

85 secAvg Time/Q

8Topics

Easy 30% Medium 44% Hard 26%

Why Practise These MCQs?

CBSE Class XNTSEState BoardsOlympiad

Triangles MCQs cover two distinct skill sets: conceptual (stating theorems, identifying criteria) and numerical (ratios, areas, unknown sides). CBSE Boards include 5-mark proof questions AND 1-mark MCQs from this chapter every year. BPT (Thales theorem) and Pythagoras are the most tested. NTSE Geometry heavily draws from similarity and ratio concepts. Olympiad problems involve elegant similarity chains.

Topic-wise MCQ Breakdown

Similar Figures (Concept)4 Q

Basic Proportionality Theorem (BPT)10 Q

Converse of BPT5 Q

Criteria for Similarity (AA, SAS, SSS)9 Q

Areas of Similar Triangles7 Q

Pythagoras Theorem9 Q

Converse of Pythagoras4 Q

Mixed Similarity + Pythagoras2 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{BPT: DE} \parallel \text{BC} \Rightarrow AD/DB = AE/EC$

$\triangle ABC \sim \triangle PQR \Rightarrow AB/PQ = BC/QR = CA/RP$

$\text{Area ratio} = (\text{side ratio})^2$

$AB^2 = AC^2 + BC^2\ (\text{Pythagoras})$

$\text{Converse: }AC^2+BC^2=AB^2 \Rightarrow \angle C=90°$

MCQ Solving Strategy

For BPT MCQs, set up the proportion immediately — DE||BC gives AD/DB = AE/EC, and you can cross-multiply to find unknowns. For similarity, state the criterion (AA/SAS/SSS) explicitly before computing the ratio. For area of similar triangles, the ratio of areas equals the SQUARE of the ratio of corresponding sides — not the ratio itself. For Pythagoras, always identify which side is the hypotenuse (opposite the right angle).

⚠ Common Traps & Errors

⚠BPT gives AD/DB, not AD/AB — be precise about which segments
⚠AA criterion requires only 2 angles — the third follows automatically
⚠Area ratio = k² where k is the side ratio — students often forget to square
⚠Pythagoras: hypotenuse is the LONGEST side, always opposite 90°
⚠Converse: if c² = a²+b², angle opposite c is 90° — not angle opposite a

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify similar triangles by AA, state BPT, basic Pythagoras

② Medium

BPT numericals, area ratio calculations, find unknown sides

③ Hard

Multi-step similarity chains, combined BPT + Pythagoras problems

★ PYQ

CBSE — proof of BPT/Pythagoras + numerical; NTSE — ratio geometry

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Coordinate Geometry

🎯 Knowledge Check

Maths — Triangles

50 Questions Class 10 MCQs

If in two triangles, their corresponding angles are equal, then the triangles are:

a a. Congruent b b. Similar c c. Right-angled d d. Isosceles

In triangle $ABC$, if $DE \parallel BC$ and $D,\ E$ lie on $AB$ and $AC$ respectively, then $AD/DB =$

a a. AC/CE b b. AE/EC c c. AB/AC d d. AD/BC

The Basic Proportionality Theorem is also known as:

a a. Pythagoras theorem b b. Heron’s theorem c c. Thales' theorem d d. Mid-point theorem

If two triangles are similar, then the ratio of their areas equals:

a a. Ratio of sides b b. Square of ratio of corresponding sides c c. Sum of side ratios d d. Cube of ratio of corresponding sides

If $\mathrm{\Delta ABC \sim \Delta DEF}$ and $AB/DE = 2/3$, area ratio = ?

a a. 2/3 b b. 4/9 c c. 3/2 d d. 9/4

In $\Delta ABC$, if $\angle A = \angle D$ and $\angle B = \angle E$, then triangles are similar by:

a a. SSS b b. SAS c c. AA d d. RHS

A line parallel to one side of a triangle divides the other two sides:

a a. Equally b b. Unequally c c. Proportionally d d. At midpoints only

If $\Delta ABC \sim \Delta PQR$ and $AB = 4\ cm,\ PQ = 2\ cm$, scale factor =

a a. 1/2 b b. 2 c c. 4 d d. 1/4

If triangles $\mathrm{\Delta ABC \sim \Delta DEF}$ are similar, $\angle A$ corresponds to:

a a. $\angle D$ b b. $\angle E$ c c. $\angle F$ d d. Any angle

In similar triangles, perimeters are in the ratio of:

a a. Areas b b. Cubes of sides c c. Corresponding sides d d. Are equal

Two sides proportional + included angle equal gives:

a a. SSS similarity b b. SAS similarity c c. AA similarity d d. RHS similarity

In$\Delta ABC,\ DE \parallel BC$. If $AD = 3$ and $DB = 6,\ AE/EC =$

a a. 1/3 b b. 1/2 c c. 2 d d. 3

If $\mathrm{\Delta ABC \sim \Delta DEF}$, then AB/DE = BC/EF = AC/DF, triangles are similar by:

a a. SAS b b. SSS c c. AA d d. RHS

A line joining midpoints of two sides of a triangle is:

a a. Equal to the third side b b. Half of the third side c c. Parallel to third side d d. Both b and c

If area ratio = 9/4 for similar triangles, side ratio =

a a. 2/3 b b. 3/2 c c. 9/4 d d. 4/9

A line dividing two sides proportionally must be:

a a. A median b b. Parallel to third side c c. A bisector d d. An altitude

If AC = 10 and QR = 5 in similar triangles, scale factor =

a a. 1/2 b b. 2 c c. 5 d d. 10

Not a similarity criterion:

a a. AA b b. SAS c c. SSS d d. SSA

If DE ∥ BC and AD/DB = 5/3, then AE/EC =

a a. 3/5 b b. 5/3 c c. 1 d d. None

Sum of angles in similar triangles:

a a. Changes b b. Remains same c c. Becomes double d d. Becomes half

If $\mathrm{\Delta ABC \sim \Delta DEF}$ and $\mathrm{AB = 6,\ DE = 3}$ in similar triangles, side ratio =

a a. 1/3 b b. 3 c c. 2 d d. 1/2

In $\mathrm{\Delta ABC,\ DE ∥ BC}$. If $\small\mathrm{AE = 4,\ EC = 8,\ AD = 3,\ DB =}$

a a. 4 b b. 6 c c. 3 d d. 2

Which triangle cannot be similar to a right triangle?

a a. Acute triangle b b. Obtuse triangle c c. Equilateral d d. Right triangle

If $\mathrm{\Delta ABC \sim \Delta PQR}$ and $\mathrm{AB = 5,\ PQ = 15}$ and triangles are similar, $\mathrm{\Delta ABC}$ is:

a a. Smaller b b. Larger c c. Equal d d. Cannot say

Similar triangles always have:

a a. Equal sides b b. Equal areas c c. Proportional corresponding sides d d. Equal medians

If $\mathrm{\Delta ABC \sim \Delta PQR}$ and $\mathrm{AB/BC = PQ/QR}$ and included angles equal:

a a. Triangles are similar b b. Triangles may not be similar c c. Triangles are congruent d d. None

If median, altitude, and angle bisector from same vertex coincide, triangle is:

a a. Right-angled b b. Scalene c c. Isosceles d d. Obtuse

if $\mathrm{\Delta ABC \sim \Delta DEF}$ $\mathrm{AC/DF = 12/4 = 3}$ in similar triangles. Area ratio =

a a. 9 b b. 3 c c. 12 d d. 36

Property true for similar polygons:

a a. All sides equal b b. All angles equal c c. Corresponding sides proportional d d. None

Triangles with proportional sides but unequal angles are:

a a. Similar b b. Not similar c c. Congruent d d. Right angled

If $\Delta ABC \sim \Delta XYZ$ and $\angle A = 50°, \angle X =$

a a. 50° b b. 60° c c. 40° d d. 30°

If $\mathrm{\Delta ABC \sim \Delta PQR}$ and $\mathrm{AB/PQ = 2}$, $\mathrm{BC = 10 ,\ QR =}$

a a. 5 b b. 10 c c. 20 d d. 8

In $\Delta ABC,\ DE \parallel BC.$ If $AD = 2,\ DB = 8,$ $AE = 3,\ EC =$

a a. 12 b b. 8 c c. 3 d d. 15

Ratio of medians in similar triangles equals:

a a. Square of side ratio b b. Side ratio c c. Area ratio d d. Perimeter ratio

A triangle similar to a right triangle must be:

a a. Any triangle b b. Right triangle c c. Obtuse triangle d d. Equilateral

If scale factor is 1/3, big triangle side/small triangle side =

a a. 3 b b. 1/3 c c. 1/9 d d. 9

If $\mathrm{\Delta ABC \sim \Delta DEF}$ and $\mathrm{AB/DE = 7/14 = 1/2}$, so area ratio =

a a. 1/2 b b. 1/4 c c. 2 d d. 4

Ratio of altitudes in similar triangles =

a a. Area ratio b b. Side ratio c c. Equal d d. Square of side ratio

If AD/DB = 9/3 = 3, AE/EC =

a a. 3 b b. 1/3 c c. 9 d d. None

Ratio of corresponding heights in similar triangles =

a a. Side ratio b b. Area ratio c c. Same d d. Always 1

Two equilateral triangles are always:

a a. Congruent b b. Similar c c. Right-angled d d. Obtuse

If $\mathrm{\Delta ABC \sim \Delta PQR}$ and $\mathrm{\angle B = 40^\circ,\ ∠Q =}$

a a. 40° b b. 60° c c. 20° d d. 30°

If $\mathrm{\Delata ABC \sim \Delta DEF}$ $\mathrm{AC/DF}$ = 12/4 = 3; $\mathrm{EC}$ = 10/3 =

a a. 5 b b. 20 c c. 10 d d. 15

If one triangle has $\mathrm{\angle A = 90^\circ}$, similar triangle must be:

a a. Obtuse b b. Acute c c. Right-angled d d. Equilateral

AB/DE = BC/EF = 4/5 indicates:

a a. SSS similarity b b. SAS similarity c c. AA similarity d d. RHS

Ratio of angle bisectors in similar triangles =

a a. Ratio of corresponding sides b b. Ratio of areas c c. Square ratio d d. Cube ratio

Side ratio = 3/1, area ratio =

a a. 3 b b. 6 c c. 9 d d. 12

A line dividing two sides in the same ratio must be:

a a. A median b b. Parallel to the third side c c. An angle bisector d d. A perpendicular bisector

Side ratio = 5/2, area ratio =

a a. 5/2 b b. 25/4 c c. 4/25 d d. 2/5

If scale factor = 3 (from smaller to larger) and EF = 6, BC =

a a. 18 b b. 6 c c. 12 d d. 3

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Frequently Asked Questions

A triangle is a closed figure formed by three line segments and has three vertices, three sides, and three angles.

When two triangles have the same shape and size, their corresponding sides and angles are equal; they are said to be congruent.

The main congruence rules are SSS, SAS, ASA, AAS, and RHS for right triangles.

Two triangles are similar if their corresponding angles are equal and corresponding sides are in proportion.

AAA / AA, SAS similarity, and SSS similarity.

If two angles of one triangle are equal to two angles of another, the triangles are similar.

If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides the sides proportionally.

Thales’ Theorem is another name for the Basic Proportionality Theorem (BPT).

If a line divides any two sides of a triangle in the same ratio, the line must be parallel to the third side.

In a right-angled triangle: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

If for a triangle $a^2 + b^2 = c^2$, the triangle is right-angled.

The ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

The sides and angles that occupy the same relative position in congruent or similar triangles.

By showing the ratio of all three pairs of corresponding sides is equal.

If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle, the triangles are congruent.

triangless – Learning Resources

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

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Triangles

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — Triangles

Frequently Asked Questions

Q 01 What is a triangle?

Q 02 What is meant by congruence of triangles?

Q 03 What are the main congruence rules studied in Class X?

Q 04 What is similarity of triangles?

Q 05 What are the similarity criteria for triangles?

Q 06 What is the AA similarity criterion?

Q 07 State the Basic Proportionality Theorem (BPT).

Q 08 What is Thales’ Theorem?

Q 09 State the converse of BPT.

Q 10 What is Pythagoras Theorem?

Q 11 What is the Converse of Pythagoras Theorem?

Q 12 What is the area ratio theorem?

Q 13 What is meant by corresponding parts of triangles?

Q 14 How do we prove triangles similar using SSS?

Q 15 What is the RHS congruence criterion?

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