Triangles Exemplar — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Triangles Exemplar" — 5 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Triangles Exemplar" — 5 important questions with detailed answers for CBSE board e…

By Syllab.in · Updated Jun 17, 2026

Key Questions Covered:

In triangle ABC, DE || BC. If AD = 3 cm, DB = 2 cm, AE = 4.5 cm, find EC.
Two isosceles triangles have equal angles. Are they similar? Justify.
Triangles ABC and PQR are similar with AB/PQ = 2/3. If area of ABC is 36 cm²,…
In a right triangle, altitude from right angle to hypotenuse divides it into …
Prove that if two triangles have equal areas and one pair of sides equal, the…

Solutions Summary:

Question	Status
In triangle ABC, DE \|\| BC. If AD = 3 cm, DB = 2 cm, AE = …	✓ Solved
Two isosceles triangles have equal angles. Are they simil…	✓ Solved
Triangles ABC and PQR are similar with AB/PQ = 2/3. If ar…	✓ Solved
In a right triangle, altitude from right angle to hypoten…	✓ Solved
Prove that if two triangles have equal areas and one pair…	✓ Solved

Showing 5 of 5 questions

Q1: In triangle ABC, DE || BC. If AD = 3 cm, DB = 2 cm, AE = 4.5 cm, find EC.

By basic proportionality theorem (Thales): AD/DB = AE/EC. So 3/2 = 4.5/EC. Thus EC = (4.5 × 2)/3 = 9/3 = 3 cm.

Q2: Two isosceles triangles have equal angles. Are they similar? Justify.

Yes. In isosceles triangle, if vertex angle is equal, base angles are also equal (property of isosceles triangle). If all angles are equal, triangles are similar by AA criterion.

Q3: Triangles ABC and PQR are similar with AB/PQ = 2/3. If area of ABC is 36 cm², find area of PQR.

Ratio of areas = (ratio of corresponding sides)². Area of PQR/Area of ABC = (PQ/AB)^2 = (3/2)^2 = 9/4. So Area of PQR = 36 × 9/4 = 81 cm².

Q4: In a right triangle, altitude from right angle to hypotenuse divides it into segments 2 cm and 8 cm. Find the altitude.

Altitude h from right angle to hypotenuse: h² = product of segments = 2 × 8 = 16. So h = 4 cm.

Q5: Prove that if two triangles have equal areas and one pair of sides equal, then altitudes to those sides are equal.

Area = (1/2) × base × height. If areas are equal and bases (sides) are equal, then heights must be equal. A1 = (1/2)b1h1, A2 = (1/2)b2h2. If A1 = A2 and b1 = b2, then h1 = h2.

Showing 5 of 5 questions. Visit the full page for complete solutions.