Answer:
The proof is explained below :
Step-by-step explanation:
We are given two lines 'h' and 'k' which are parallel to each other. Also, there is another line 'j' that is perpendicular to line 'h'.
To Prove : line 'j' is perpendicular to line 'k'.
Proof : Let m, n and p be the slopes of lines 'h', 'k' and 'j' respectively.
Now, since line 'h' and 'k' are parallel, so their slopes will be equal. i.e., m = n .............(1)
Also, lines 'h' and 'j' are perpendicular, so the product of their slopes is -1. i.e., m × p = -1.
Or we can write it as n × p = -1 ...............From equation (1)
Thus, the line 'j' is perpendicular to line 'k'.
Hence Proved
