A B C D E DE ∥ BC AD/DB = AE/EC Area ratio = k² AB²=AC²+BC²
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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

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
1
If in two triangles, their corresponding angles are equal, then the triangles are:
2
In triangle \(ABC\), if \(DE \parallel BC\) and \(D,\ E\) lie on \(AB\) and \(AC\) respectively, then \(AD/DB =\)
3
The Basic Proportionality Theorem is also known as:
4
If two triangles are similar, then the ratio of their areas equals:
5
If \(\mathrm{\Delta ABC \sim \Delta DEF}\) and \(AB/DE = 2/3\), area ratio = ?
6
In \(\Delta ABC\), if \(\angle A = \angle D\) and \(\angle B = \angle E\), then triangles are similar by:
7
A line parallel to one side of a triangle divides the other two sides:
8
If \(\Delta ABC \sim \Delta PQR\) and \(AB = 4\ cm,\ PQ = 2\ cm\), scale factor =
9
If triangles \(\mathrm{\Delta ABC \sim \Delta DEF}\) are similar, \(\angle A\) corresponds to:
10
In similar triangles, perimeters are in the ratio of:
11
Two sides proportional + included angle equal gives:
12
In\(\Delta ABC,\ DE \parallel BC\). If \(AD = 3\) and \(DB = 6,\ AE/EC =\)
13
If \(\mathrm{\Delta ABC \sim \Delta DEF}\), then AB/DE = BC/EF = AC/DF, triangles are similar by:
14
A line joining midpoints of two sides of a triangle is:
15
If area ratio = 9/4 for similar triangles, side ratio =
16
A line dividing two sides proportionally must be:
17
If AC = 10 and QR = 5 in similar triangles, scale factor =
18
Not a similarity criterion:
19
If DE ∥ BC and AD/DB = 5/3, then AE/EC =
20
Sum of angles in similar triangles:
21
If \(\mathrm{\Delta ABC \sim \Delta DEF}\) and \(\mathrm{AB = 6,\ DE = 3}\) in similar triangles, side ratio =
22
In \(\mathrm{\Delta ABC,\ DE ∥ BC}\). If \(\small\mathrm{AE = 4,\ EC = 8,\ AD = 3,\ DB =}\)
23
Which triangle cannot be similar to a right triangle?
24
If \(\mathrm{\Delta ABC \sim \Delta PQR}\) and \(\mathrm{AB = 5,\ PQ = 15}\) and triangles are similar, \(\mathrm{\Delta ABC}\) is:
25
Similar triangles always have:
26
If \(\mathrm{\Delta ABC \sim \Delta PQR}\) and \(\mathrm{AB/BC = PQ/QR}\) and included angles equal:
27
If median, altitude, and angle bisector from same vertex coincide, triangle is:
28
if \(\mathrm{\Delta ABC \sim \Delta DEF}\) \(\mathrm{AC/DF = 12/4 = 3}\) in similar triangles. Area ratio =
29
Property true for similar polygons:
30
Triangles with proportional sides but unequal angles are:
31
If \(\Delta ABC \sim \Delta XYZ\) and \(\angle A = 50°, \angle X =\)
32
If \(\mathrm{\Delta ABC \sim \Delta PQR}\) and \(\mathrm{AB/PQ = 2}\), \(\mathrm{BC = 10 ,\ QR =}\)
33
In \(\Delta ABC,\ DE \parallel BC.\) If \(AD = 2,\ DB = 8,\) \(AE = 3,\ EC =\)
34
Ratio of medians in similar triangles equals:
35
A triangle similar to a right triangle must be:
36
If scale factor is 1/3, big triangle side/small triangle side =
37
If \(\mathrm{\Delta ABC \sim \Delta DEF}\) and \(\mathrm{AB/DE = 7/14 = 1/2}\), so area ratio =
38
Ratio of altitudes in similar triangles =
39
If AD/DB = 9/3 = 3, AE/EC =
40
Ratio of corresponding heights in similar triangles =
41
Two equilateral triangles are always:
42
If \(\mathrm{\Delta ABC \sim \Delta PQR}\) and \(\mathrm{\angle B = 40^\circ,\ ∠Q =}\)
43
If \(\mathrm{\Delata ABC \sim \Delta DEF}\) \(\mathrm{AC/DF}\) = 12/4 = 3; \(\mathrm{EC}\) = 10/3 =
44
If one triangle has \(\mathrm{\angle A = 90^\circ}\), similar triangle must be:
45
AB/DE = BC/EF = 4/5 indicates:
46
Ratio of angle bisectors in similar triangles =
47
Side ratio = 3/1, area ratio =
48
A line dividing two sides in the same ratio must be:
49
Side ratio = 5/2, area ratio =
50
If scale factor = 3 (from smaller to larger) and EF = 6, BC =
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Class 10 Maths Triangles 50 MCQs 🔥 NCERT Chapter 6 Practice Questions with Answers
Class 10 Maths Triangles 50 MCQs 🔥 NCERT Chapter 6 Practice Questions with Answers — Complete Notes & Solutions · academia-aeternum.com
Mastering the chapter Triangles is essential for building strong foundational skills in geometry at the Class X level. These MCQs are thoughtfully crafted to help learners explore every dimension of triangle similarity, proportionality, the Basic Proportionality Theorem, and the core relationships that govern geometric figures. Each question is designed to sharpen conceptual clarity while reinforcing analytical thinking—skills that are indispensable for board examinations and competitive…
🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Class 10 Maths Triangles 50 MCQs 🔥 NCERT Chapter 6 Practice Questions with Answers
    Class 10 Maths Triangles 50 MCQs 🔥 NCERT Chapter 6 Practice Questions with Answers — Complete Notes & Solutions · academia-aeternum.com
    Mastering the chapter Triangles is essential for building strong foundational skills in geometry at the Class X level. These MCQs are thoughtfully crafted to help learners explore every dimension of triangle similarity, proportionality, the Basic Proportionality Theorem, and the core relationships that govern geometric figures. Each question is designed to sharpen conceptual clarity while reinforcing analytical thinking—skills that are indispensable for board examinations and competitive…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    Threads
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    academia-aeternum.com/class-10/mathematics/triangles/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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