Appendix 1 · Proofs in Mathematics

NCERT Class 10 Maths Exercise A1.5

All 2 questions of NCERT Class 10 Maths Exercise A1.5 (Proofs in Mathematics), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Write ​the converses ​of the following statements.

   1. (i)If it ​is hot in Tokyo, then Sharan sweats a lot.
   2. (ii)If Shalini is hungry, then ​her stomach ​grumbles.
   3. (iii)If Jaswant has a scholarship, then she can get a degree.
   4. (iv)If a plant has flowers, then it is alive.
   5. (v)If an animal ​is a ​cat, then it has a tail.
   Show answer

   (i) If Sharan sweats a lot, then it is hot in Tokyo. (ii) If Shalini’s stomach grumbles, then she is hungry. (iii) If Jaswant can get a degree, then she has a scholarship. (iv) If a plant is alive, then it has flowers. (v) If an animal has a tail, then it is a cat.

   Step-by-step solution →
2. Q2
   Write the converses ​of the following statements. ​Also, decide in each case whether the ​converse is true or false.

   1. (i)If triangle $ABC$ ​is isosceles, then its base angles are equal.
   2. (ii)If an integer is odd, then its square is an odd integer.
   3. (iii)If $x^2=1$, then $x=1$.
   4. (iv)If $ABCD$ is a parallelogram, then $AC$ and $BD$ bisect each other.
   5. (v)If $a,b$ and $c$ ​are whole numbers, then $a+(b+c)=(a+b)+c$.
   6. (vi)If $x$ and $y$ are two odd numbers, then $x+y$ is an even number.
   7. (vii)If ​vertices of ​a parallelogram lie on a ​circle, then it is a rectangle.
   Show answer

   Converses, with truth values: (i) If the base angles of triangle ABC are equal, then it is isosceles - True. (ii) If the square of an integer is odd, then the integer is odd - True. (iii) If x = 1, then x^2 = 1 - True. (iv) If AC and BD bisect each other, then ABCD is a parallelogram - True. (v) If a + (b+c) = (a+b) + c, then a, b and c are whole numbers - False. (vi) If x + y is an even number, then x and y are odd - False (e.g. 2 + 4 = 6). (vii) If a parallelogram is a rectangle, then its vertices lie on a circle - True.

   Step-by-step solution →