Question

*Which of the following action should be taken to find the points at equidistance from the end points of the segment*

1️⃣ Draw a perpendicular
2️⃣ Draw a perpendicular bisector
3️⃣ Draw angle bisector
4️⃣ None of the above​

Answer 1

Answer:

your answer is 2 may be drw a perpendicular bisector

hope it's help you

it's khushi

Answer 2

Given : A line segment

To Find :   Which of the following action should be taken to find the points at equidistance from the end points of the segment

1️⃣ Draw a perpendicular

2️⃣ Draw a perpendicular bisector

3️⃣ Draw angle bisector

4️⃣ None of the above​

Solution:

A line segment is there

Draw a perpendicular is not sufficient information as not defined where to draw perpendicular.

If Perpendicular is drawn at mid point of segment then  points will be at equidistance from the end points of the segment

Perpendicular at Mid point is called perpendicular bisector

Hence option 2️⃣ Draw a perpendicular bisector  is correct answer

There is no angle as only one line segment is there hence there is no meaning of drawing angle bisector

Proof that points are equidistant at perpendicular bisector from the  end points of the segment

AB is a segment

XY is the perpendicular bisector intersecting AB at M

=> AM = BM   and   ∠AMX = ∠AMY = ∠BMX = ∠BMY = 90°

Lets take a point P on  XY

ΔAMP and ΔBMP

AM = BM

∠AMP =   ∠BMP =   90°

MP = MP

=> ΔAMP ≅ ΔBMP  ( using SAS congruence)

Corresponding parts of congruent triangles are congruent

=> AP = BP

Hence Proved points are equidistant at perpendicular bisector from the  end points of the segment

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