Question

1. triangle abc is isosceles. use straightedge and compass tools to construct the perpendicular bisector for segment ab.

Explanation:

Step1: Set compass width

Open the compass wider than half - the length of segment $AB$.

Step2: Draw arcs from A

Place the compass at point $A$ and draw arcs above and below segment $AB$.

Step3: Draw arcs from B

Without changing the compass width, place the compass at point $B$ and draw arcs above and below segment $AB$ to intersect the arcs drawn from point $A$.

Step4: Draw the bisector

Use the straightedge to draw a line through the two intersection points of the arcs. This line is the perpendicular bisector of segment $AB$.

Answer:

The constructed line through the intersection of the arcs above and below segment $AB$ is the perpendicular bisector of $AB$.