Question

Use the following line segment to construct a line segment that is double the length of AB on a new line and label the duplicated segment CD.

a) Measure the midpoint of AB and construct a perpendicular bisector.
b) Extend AB to a point E and construct a line through E parallel to AB.
c) Draw a ˚le with center A and radius AB, intersecting AB at point C, and then connect AC.
d) Construct a right-angled triangle with sides AB, BC, and AC.

Answer 1

To construct a line segment double the length of AB, one must find the midpoint of AB, extend AB and draw a circle with AB's length as the radius, and connect points to form a right-angled triangle.

Step-by-step explanation:

The task involves constructing a line segment that is twice the length of a given line segment AB. Here's how you can achieve this:

Step-by-Step Construction

1. First, find the midpoint of AB and construct a perpendicular bisector. This will divide AB into two equal parts.
2. Extend AB to a new point E, making sure that AE is equal in length to AB (AE = AB), and construct a line through E that is parallel to AB.
3. With A as the center and AB as the radius, draw a circle intersecting AB at point C—your new line segment AC will be equal to AB.
4. Finally, connect points A, B, and C to form a right-angled triangle with AB and AC as the legs, and BC as the hypotenuse, satisfying the Pythagorean theorem.

To summarize, by using basic geometric constructions—perpendicular bisectors, parallel lines, and circles—you can easily duplicate a line segment and create one that is double the length of the original.