Class 10 • Maths • Chapter 6
Triangles
True & False Quiz
Similar. Proportional. Congruent.
✓True
✗False
25
Questions
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Ch.6
Chapter
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X
Class
Why True & False for Triangles?
How this format sharpens your conceptual clarity
🔵 Triangle similarity is the foundation of trigonometry, coordinate geometry and mensuration — it links proportions to reality.
✅ T/F focuses on the Basic Proportionality Theorem (Thales), similarity criteria, and the ratio of areas theorem.
🎯 Similar triangles have equal angles AND proportional sides — congruent triangles are a SPECIAL CASE of similar (ratio = 1).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The Basic Proportionality Theorem (Thales' theorem) states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides in the same ratio.
Q 2
In a triangle, a line parallel to one side always intersects the other two sides externally.
Q 3
The converse of the Basic Proportionality Theorem is valid, meaning if a line divides two sides of a triangle proportionally, it must be parallel to the third side.
Q 4
Triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Q 5
Two triangles with two pairs of equal corresponding angles are always similar.
Q 6
The SSS similarity criterion states that three sides of one triangle are proportional to three sides of another triangle implies similarity.
Q 7
SAS similarity holds if two sides of one triangle are proportional to two sides of another and the included angles are equal.
Q 8
All congruent triangles are similar.
Q 9
The ratio of areas of two similar triangles equals the square of the ratio of their corresponding sides.
Q 10
In right-angled triangles, the square of the hypotenuse equals the sum of squares of the other two sides.
Q 11
The converse of Pythagoras theorem is false for right-angled triangles.
Q 12
A line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long.
Q 13
Similar triangles always have equal areas.
Q 14
If two triangles have all three angles equal, their sides must be equal in length.
Q 15
In \(\mathrm{\Delta ABC}\) and \(\mathrm{\Delta DEF}\), if \(\mathrm{AB/DE = BC/EF}\) but angles at \(\mathrm{B}\) and \(\mathrm{E}\) differ, the triangles cannot be similar.
Q 16
The Basic Proportionality Theorem applies only to equilateral triangles.
Q 17
Pythagoras theorem applies to any triangle, not just right-angled ones.
Q 18
Areas of similar triangles are proportional to the product of their corresponding sides.
Q 19
A triangle with sides 3, 4, 5 cm satisfies Pythagoras theorem.
Q 20
In similar triangles, corresponding altitudes are proportional to their sides.
Q 21
The AAA similarity criterion requires all three angles to be equal.
Q 22
If \(\mathrm{DE \parallel BC}\) in \(\mathrm{\Delta ABC}\), then \(\mathrm{\Delta ADE \sim \Delta ABC}\) by AAA similarity.
Q 23
Two triangles with equal perimeters must be similar.
Q 24
The ratio of areas of \(\mathrm{\Delta ABC}\) to \(\mathrm{\Delta DEF}\) is 4:9 if their similarity ratio is 3:2.
Q 25
Pythagoras theorem can prove if a triangle is isosceles right-angled.
Key Takeaways — Triangles
Core facts for CBSE Boards & exams
1
BPT (Thales): If DE ∥ BC in △ABC, then AD/DB = AE/EC.
2
Similarity criteria: AA, SSS, SAS — only these three suffice.
3
Ratio of areas of similar triangles = square of ratio of corresponding sides.
4
In a right triangle, the altitude to the hypotenuse creates two similar triangles.
5
Pythagoras Theorem: AC² = AB² + BC² (provable using similarity).
6
Converse of Pythagoras: if AC² = AB² + BC², then ∠B = 90°.