Answer the following: Q 1 Find counter-examples to disprove the following statements: (i) If the corresponding angles in two - Maths - Playing with Numbers

Question

Answer the following:
Q 1 Find counter-examples to disprove the following
statements:
(i) If the corresponding angles in two triangles are equal, then
the triangles are congruent
(ii) 2 n 2 + 11 is a prime for all whole numbers n
(iii) n 2 - n + 41 is a prime for all positive integers n

Sanjari Kalantri · Accepted Answer

Dear Student,

i Let there be two equilateral triangles, one of side 6 cm and the other of side 4 cm
 Their corresponding angles are all equal - as each angle is 60°
 However, the two triangles are not congruent, as they don't have equal sides
ii When n = 11, 2112 + 11 = 2121 + 11 = 242 + 11 = 253 = 23 × 11, which is not primeiii When n = 41, 412 - 41 + 41 = 1681 = 41 × 41, which is not prime

Answer the following: Q.1. Find counter-examples to disprove the following statements: (i) If the corresponding angles in two triangles are equal, then the triangles are congruent. (ii) 2 n 2 + 11 is a prime for all whole numbers n. (iii) n 2 - n + 41 is a prime for all positive integers n.

Answer the following:
Q.1. Find counter-examples to disprove the following statements:
(i) If the corresponding angles in two triangles are equal, then the triangles are congruent.
(ii) $2 n^{2} + 11$ is a prime for all whole numbers n.
(iii) $n^{2} - n + 41$ is a prime for all positive integers n.