Question

you are given ∠bad and asked to copy it using only a compass and a straightedge. the new angle will be ∠tom. drag the steps below into the correct order to complete the construction of the copied angle. answer measure the distance between points b and d. without changing the width of the compass, place the compass on point m and draw a second arc that intersects the first. label the intersection point draw a ray. label the end point o. draw an arc with center a that intercepts both rays with endpoint a. label the

Explanation:

To solve the problem of ordering the steps to copy \(\angle BAD\) as \(\angle TOM\) using a compass and straightedge, we follow the standard angle - copying construction steps:

Step 1: Draw a ray. Label the end - point \(O\)

We first need a starting ray for our new angle \(\angle TOM\). The endpoint of this ray will be \(O\), and this ray will be one of the sides of the new angle.

Step 2: Draw an arc with center \(A\) that intercepts both rays with endpoint \(A\). Label the intersection points (let's say the intersection with \(AB\) is \(B\) and with \(AD\) is \(D\))

This step is used to mark the "opening" of the original angle \(\angle BAD\). By drawing an arc centered at \(A\) that cuts both sides of the angle, we are recording the length of the arc between the two sides of the original angle.

Step 3: Measure the distance between points \(B\) and \(D\) (or equivalently, we can use the compass to set the width to the distance between the two intersection points on the arc of the original angle)

We need to transfer the "size" of the original angle's opening. Measuring the distance between \(B\) and \(D\) (or using the compass to capture the length of the arc between the two intersection points on the original angle's arc) allows us to replicate this opening in the new angle.

Step 4: Without changing the width of the compass, place the compass on point \(M\) and draw a second arc that intersects the first. Label the intersection point (let's say \(P\))

After we have set the compass width to the length of the arc in the original angle, we place the compass on point \(M\) (on the ray we drew in step 1) and draw an arc. The intersection of this arc with the arc we will draw centered at \(O\) (with the same radius as the arc centered at \(A\)) will give us the point that determines the other side of the new angle. Then we can draw the ray from \(O\) through this intersection point to complete the angle \(\angle TOM\).

The correct order of the steps is:

1. Draw a ray. Label the end point \(O\).
2. Draw an arc with center \(A\) that intercepts both rays with endpoint \(A\). Label the intersection points.
3. Measure the distance between points \(B\) and \(D\).
4. Without changing the width of the compass, place the compass on point \(M\) and draw a second arc that intersects the first. Label the intersection point.

Answer:

To solve the problem of ordering the steps to copy \(\angle BAD\) as \(\angle TOM\) using a compass and straightedge, we follow the standard angle - copying construction steps:

Step 1: Draw a ray. Label the end - point \(O\)

We first need a starting ray for our new angle \(\angle TOM\). The endpoint of this ray will be \(O\), and this ray will be one of the sides of the new angle.

Step 2: Draw an arc with center \(A\) that intercepts both rays with endpoint \(A\). Label the intersection points (let's say the intersection with \(AB\) is \(B\) and with \(AD\) is \(D\))

This step is used to mark the "opening" of the original angle \(\angle BAD\). By drawing an arc centered at \(A\) that cuts both sides of the angle, we are recording the length of the arc between the two sides of the original angle.

Step 3: Measure the distance between points \(B\) and \(D\) (or equivalently, we can use the compass to set the width to the distance between the two intersection points on the arc of the original angle)

We need to transfer the "size" of the original angle's opening. Measuring the distance between \(B\) and \(D\) (or using the compass to capture the length of the arc between the two intersection points on the original angle's arc) allows us to replicate this opening in the new angle.

Step 4: Without changing the width of the compass, place the compass on point \(M\) and draw a second arc that intersects the first. Label the intersection point (let's say \(P\))

After we have set the compass width to the length of the arc in the original angle, we place the compass on point \(M\) (on the ray we drew in step 1) and draw an arc. The intersection of this arc with the arc we will draw centered at \(O\) (with the same radius as the arc centered at \(A\)) will give us the point that determines the other side of the new angle. Then we can draw the ray from \(O\) through this intersection point to complete the angle \(\angle TOM\).

The correct order of the steps is:

1. Draw a ray. Label the end point \(O\).
2. Draw an arc with center \(A\) that intercepts both rays with endpoint \(A\). Label the intersection points.
3. Measure the distance between points \(B\) and \(D\).
4. Without changing the width of the compass, place the compass on point \(M\) and draw a second arc that intersects the first. Label the intersection point.