Amari constructed ray ZR, a line segment bisector of XY.

Question

If the length of XY is 10cm, what is the length of XZ?

Answer 1

If ray ZR is a bisector of line segment XY, it means that it divides XY into two equal parts. Since the length of XY is 10 cm, we can calculate the length of XZ as follows:

\[ XZ = \frac{XY}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]

Therefore, the length of XZ is 5 cm.

Answer 2

What is the construction that needs to be done to make a copy of angle LJK?

Answer 3

To copy an angle \( LJK \), you can follow these steps:

Materials Needed:

• A compass
• A straightedge (ruler without markings)
• A pencil

Steps to Copy the Angle:

1. Draw a Ray:

   • Start by drawing a ray \( QR \) where you want to copy the angle.

2. Set the Compass Width:

   • Place the compass point at vertex \( J \) of angle \( LJK \) and draw an arc that intersects both rays \( LJ \) and \( JK \). This intersection will create points \( A \) and \( B \) on those rays.

3. Measure the Arc:

   • Without changing the compass width, take the same compass and place the point at point \( Q \) on ray \( QR \). Draw a similar arc that intersects ray \( QR \). Label the intersection point as \( C \).

4. Copy the Arc:

   • Measure the distance between points \( A \) and \( B \) (the angle arc from the original angle) using the compass.
   • Keeping the same compass width, place the compass point on point \( C \) and draw an arc that intersects the arc you drew in step 3. Label the intersection point \( D \).

5. Draw the Lines:

   • Now, draw a straight line from \( Q \) through point \( C \) and another line from \( C \) through point \( D \). The angle \( QCD \) is a copy of angle \( LJK \).

Summary:

You have successfully copied angle \( LJK \) at point \( Q \) on ray \( QR \) using a compass and straightedge. The process uses the properties of equal arc lengths to ensure angles are congruent.