CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Exemplar Solutions Class 10 Maths Chapter 6 Triangles
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Boards begin February 2027
Pre-boards are in December
Triangles is in Geometry, which carries 15 of the 80 marks in the 2026-27 CBSE Maths paper
14 NCERT Exemplar questions from Chapter 6
Exercise 6.1
Exemplar Ex 6.1 Q31 mark
If △ABC ~ △EDF and △ABC is not similar to △DEF, then which of the following is NOT true?
Step 1△ABC ~ △EDF means A↔E, B↔D, C↔F. So AB/ED = BC/DF = CA/FE.
Step-by-step solution
△ABC ~ △EDF means A↔E, B↔D, C↔F. So AB/ED = BC/DF = CA/FE.
From AB/ED = BC/DF: AB · DF = ED · BC ⇒ option (d) BC · DE = AB · FD is TRUE.
From BC/DF = CA/FE: BC · FE = DF · CA ⇒ option (a) BC · EF = AC · FD is TRUE.
From AB/ED = CA/FE: AB · FE = ED · CA ⇒ option (b) AB · EF = AC · DE is TRUE.
Option (c) BC · DE = AB · EF would require a different correspondence and is NOT a consequence of △ABC ~ △EDF.
Two line segments AC and BD intersect at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then ∠PBA equals:
Is the following statement true? Why? 'Two quadrilaterals are similar if their corresponding angles are equal.'
Step 1Definition: two polygons of the same number of sides are similar iff BOTH (i) corresponding angles are equal AND (ii) corresponding sides are proportional.
Step-by-step solution
Definition: two polygons of the same number of sides are similar iff BOTH (i) corresponding angles are equal AND (ii) corresponding sides are proportional.
Counter-example: a 2×2 square and a 2×5 rectangle — both have all angles 90°, but sides give ratios 2:2 = 1 and 2:5 = 0.4, not equal.
Therefore equal angles alone do not guarantee similarity for quadrilaterals.
Answer:False — equal angles are necessary but not sufficient (counter-example: square vs rectangle).
If in two right triangles one of the acute angles of one triangle is equal to an acute angle of the other triangle, can the two triangles be similar? Why?
Step 1Both triangles have a right angle (90°) — first pair of equal angles.
Step-by-step solution
Both triangles have a right angle (90°) — first pair of equal angles.
Given: one acute angle of one = one acute angle of the other — second pair of equal angles.
Two pairs of equal angles ⇒ AA similarity ⇒ triangles are similar.
Answer:Yes — by AA similarity (right angle + one equal acute angle).
A 15 m high tower casts a shadow 24 m long at a certain time, and at the same time a telephone pole casts a shadow 16 m long. Find the height of the telephone pole.
Step 1At the same time, sun's rays make equal angles with the ground. Both tower and pole are vertical.
Step-by-step solution
At the same time, sun's rays make equal angles with the ground. Both tower and pole are vertical.
By AA similarity, the two right triangles are similar.
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio. (Basic Proportionality Theorem.)
Step 1Given: △ABC; DE ∥ BC with D ∈ AB, E ∈ AC.
Step-by-step solution
Given: △ABC; DE ∥ BC with D ∈ AB, E ∈ AC.
To prove: AD/DB = AE/EC.
Construction: join BE, CD; draw perpendiculars DM ⊥ AC and EN ⊥ AB.
Compute ratios of areas: ar(△ADE)/ar(△BDE) = ((1/2)·AD·EN)/((1/2)·DB·EN) = AD/DB. (*)
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Questions from the NCERT Class 10 Mathematics Exemplar Problems; the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.