Question

Alex needs to use the perpendicular bisector method to draw a triangle with two equal sides when the side length of the third side (AB) is given.
The following statements describe the steps to draw a perpendicular bisector of the line segment AB.

Statement 1: Cut the line segment $AB$ into two equal parts.
Statement 2: Makes a ${180}^{\circ }$ angle with the line segment $AB.$

Choose the correct option.

• A. Both statements are wrong.
• B. Both statements are correct.
• C. Only statement $2$ is correct.
• D. Only statement $1$ is correct.

Answer 1

The correct option is D Only statement $1$ is correct.

Every point on the perpendicular bisector will be the same distance from both point $A$ and point $B$ and it makes a right angle with the line segment $AB.$


Let’s consider a point E on the perpendicular bisector. If we join $AE$ and $BE,$ we will get a triangle that will have exactly two equal sides. The two equal sides in the given figure are $AE$ and $BE,$ and the third side is $AB$ with a different side length.