Question

Given a segment AB and a ray CD, construct a point X on CD such that AB CX Let A, B and C be three non-collinear points. We say that △ABC is an equilateral triangle if its three sides are all congruent. Re member that neither this definition nor the corresponding diagram in Figure 1.11 guarantee the existence of three points forming an equilat- eral triangle. To show that they exist, we must construct one. FIGURE 1.11. An equilateral triangle.

Answer 1

To construct a point X on ray CD such that AB < CX, follow these steps: Draw segment AB and ray CD. Use a compass to draw an arc with center A and any radius, intersecting ray CD at point X'. Construct a ray passing through point C and X'. Draw a line parallel to ray CD through point B, intersecting the ray you just constructed at point X. Now you have point X on CD such that AB < CX.

Step-by-step explanation:

To construct a point X on ray CD such that AB < CX, you can follow these steps:

1. Draw segment AB and ray CD.
2. Use a compass to draw an arc with center A and any radius, intersecting ray CD at point X'.
3. Construct a ray passing through point C and X'.
4. Draw a line parallel to ray CD through point B, intersecting the ray you just constructed at point X.

Now you have point X on CD such that AB < CX.