Similar Triangles — Telangana (SSC) Class 10 Mathematics Solutions (Free)
Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Similar Triangles" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Similar Triangles" — important questions with detailed answers, download PDF for…
By Syllab.in · Updated
Q1: If triangle ABC is similar to triangle PQR with AB/PQ = 2/3, and area of ABC = 36 cm², find area of PQR.
Step 1: Ratio of corresponding sides = AB/PQ = 2/3
Step 2: Ratio of areas = (ratio of sides)²
Step 3: Area of ABC/Area of PQR = (2/3)² = 4/9
Step 4: 36/Area of PQR = 4/9
Step 5: Area of PQR = 36 × 9/4 = 81 cm²
Final Answer: Area of PQR = 81 cm²
Q2: In triangle ABC, D and E are points on AB and AC respectively such that DE ∥ BC. If AD = 3 cm, DB = 2 cm, AE = 4.5 cm, find EC.
Step 1: Since DE ∥ BC, by Basic Proportionality Theorem (Thales)
Step 2: AD/DB = AE/EC
Step 3: 3/2 = 4.5/EC
Step 4: EC = (4.5 × 2)/3 = 9/3 = 3 cm
Final Answer: EC = 3 cm
Q3: Prove that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
Step 1: Let triangle ABC with line DE drawn parallel to BC, D on AB, E on AC.
Step 2: We need to prove AD/DB = AE/EC
Step 3: Draw EF ∥ AB (F on BC)
Step 4: ADEF is a parallelogram, so AD = EF and AE = DF
Step 5: In triangle ABC with parallel lines, triangles ADE and ABC are similar
Step 6: By AA similarity, ∠ADE = ∠ABC and ∠AED = ∠ACB
Step 7: Therefore AD/AB = AE/AC
Step 8: This gives AD/DB = AE/EC (rearranging proportions)
Final Answer: Line parallel to one side divides other sides proportiona…
Q4: Two triangles have sides 3, 4, 5 and 6, 8, 10. Prove they are similar.
Step 1: Check if corresponding sides are proportional
Step 2: Ratio = 6/3 = 2, 8/4 = 2, 10/5 = 2
Step 3: All ratios equal 2
Step 4: By SSS (Side-Side-Side) similarity criterion, the triangles are similar
Step 5: Scale factor = 2:1
Final Answer: Triangles are similar by SSS with scale factor 2:1
Q5: If the areas of two similar triangles are 25 cm² and 36 cm², find the ratio of their corresponding sides.
Step 1: For similar triangles, Area ratio = (side ratio)²
Step 2: Area₁/Area₂ = 25/36
Step 3: (side₁/side₂)² = 25/36
Step 4: side₁/side₂ = √(25/36) = 5/6
Final Answer: Ratio of corresponding sides = 5:6
Showing 5 of 8 questions — full solutions on the page.