Question

consider two right angles triangle with sides a, b, c and A, B, C, respectively. if a/A=b/B, then show that c/C=a/A. Does the result hold when the triangles are not right angle? justify your answer ​

Answer 1

Answer:

Step-by-step explanation:

consider two right angles triangle with sides a, b, c and A, B, C, respectively. if a/A=b/B, then show that c/C=a/A

as it is an right angle triangle so

c² = a² + b²

C² = A² + B²

a/A=b/B = K

=> a = AK

    b = BK

c² = (AK)² + (BK)²

=> c² = K²(A² + B²)

=> c² = K²(C²)

Taking square rot both sides

  c = KC

=>c/C = k

hence

a/A=b/B = c/C

Triangles are similar when Corresponding sides are in proportion  or corresponding angles are equal

Result will hold true even if triangle is not right angle triangle but

corresponding angle must be equal in that case

if corresponding angles are not equal then result will not hold true