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…
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NCERT Solutions for Class 10 Mathematics — Triangles Exemplar. Step-by-step answers to all 5 textbook questions from this chapter, written for CBSE board preparation and free to use.
Triangles Exemplar — All 5 Questions Solved
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.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.