Prove that through a given point, we can draw only one perpendicular to a given line
Solution:
Consider two lines nB and mA intersecting at P
Draw a line l perpendicular to the lines
We have to prove that only one perpendicular can be drawn to a given line i.e., ∠P = 0°
Since nB is perpendicular to l,
∠B = 90°
Since mA is perpendicular to l,
∠A = 90°
Considering triangle APB,
∠A + ∠P + ∠B = 180°
90° + ∠P + 90° = 180°
180° + ∠P = 180°
∠P = 180° - 180°
∠P = 0°
This implies lines m and n coincide.
Therefore, only one perpendicular can be drawn to a given line.
✦ Try This: In the figure given above, l∥m and p∥q. Find the values of x,y and z.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.4 Problem 4
Prove that through a given point, we can draw only one perpendicular to a given line
Summary:
It is proven that through a given point, we can draw only one perpendicular to a given line by angle sum property which states that the sum of all three interior angles of a triangle is equal to 180 degrees
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