Class 10 Maths · Chapter 6

Triangles

424 Class 10 Maths questions on Triangles from the NCERT textbook, NCERT Exemplar and CBSE board papers 2018–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 22 of 22

1. Q421 CBSE 2018
   In ​an equilateral $△ABC$, $D$ ​is a point on ​the ​side $BC$ ​such that $BD=\frac{1}{3}BC$. ​Prove ​that $9A{D}^2=7A{B}^2$.
   Show answer

   $A{D}^2=\frac{7a^2}{9}$, hence $9A{D}^2=7A{B}^2$. Proved.

   Step-by-step solution →
2. Q422 CBSE 2018
   Prove ​that ​in a triangle, if the square of one side is equal to sum of ​the ​squares of the other ​two sides, the angle opposite the ​first side is ​a right angle.
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   Since $△ABC\cong △PQR$ (SSS) and $\angle PQR=90^{\circ }$, we have $\angle ABC=90^{\circ }$. Hence the angle opposite the first side is a right angle. Proved.

   Step-by-step solution →
3. Q423 CBSE 2018
   In ​an ​equilateral $△ABC$, $D$ is a point on ​side $BC$ ​such ​that $BD=\frac{1}{3}BC$. Prove ​that $9(AD{)}^2=7(AB{)}^2$.
   Show answer

   Since $A{D}^2=\frac{7a^2}{9}$ where $a=AB$, multiplying by 9 gives $9(AD{)}^2=7(AB{)}^2$. Hence proved.

   Step-by-step solution →
4. Q424 CBSE 2018
   Prove that, in a ​right ​triangle, the square on the hypotenuse is ​equal to the sum of the squares ​on ​the ​other ​two sides.
   Show answer

   In right triangle $ABC$ (right angle at $A$), $B{C}^2=A{B}^2+A{C}^2$. Hence the square on the hypotenuse equals the sum of the squares on the other two sides.

   Step-by-step solution →