Question
Omar constructed ∠CPD as a copy of ∠EOF. Which set of steps did he follow in order to construct a
copy of the angle seen in the image?
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
OF using a compass and use that length to place point D on the auxiliary
segment by placing the pointed end of the compass on point P and drawing an arc.
Step 3: Measure the length of
¯
FE using a compass and use that length to draw another smaller arc above
point D by placing the pointed end of the compass on point D.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points P and C.
Step 1: Draw auxiliary segment AB.
Step 2: Measure the length of
¯
OF using a compass and use that length to put point D on the auxiliary
segment by placing the pointed end of the compass on point P and drawing an arc.
Step 3: Measure the length using a compass and use that length to draw another smaller arc above point
D by placing the pointed end of the compass on point D.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points E and C.
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
EF using a compass and use that length to draw an arc by placing the
pointed end at point P.
Step 3: Without changing the size of the compass, draw another arc that intersects the first arc by placing
the pointed end of the compass on point C.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points E and C.
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
OF using a compass and use that length to place point D on the auxiliary
segment by drawing an arc.
Step 3: Place point C on the arc constructed.
Step 4: Draw a line connecting points E and C
copy of the angle seen in the image?
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
OF using a compass and use that length to place point D on the auxiliary
segment by placing the pointed end of the compass on point P and drawing an arc.
Step 3: Measure the length of
¯
FE using a compass and use that length to draw another smaller arc above
point D by placing the pointed end of the compass on point D.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points P and C.
Step 1: Draw auxiliary segment AB.
Step 2: Measure the length of
¯
OF using a compass and use that length to put point D on the auxiliary
segment by placing the pointed end of the compass on point P and drawing an arc.
Step 3: Measure the length using a compass and use that length to draw another smaller arc above point
D by placing the pointed end of the compass on point D.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points E and C.
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
EF using a compass and use that length to draw an arc by placing the
pointed end at point P.
Step 3: Without changing the size of the compass, draw another arc that intersects the first arc by placing
the pointed end of the compass on point C.
Step 4: Place point C at the intersection of the two arcs and draw a line connecting points E and C.
Step 1: Draw auxiliary segment AB and place point P on the auxiliary segment.
Step 2: Measure the length of
¯
OF using a compass and use that length to place point D on the auxiliary
segment by drawing an arc.
Step 3: Place point C on the arc constructed.
Step 4: Draw a line connecting points E and C
Answers
GPT-4o mini
To create a copy of angle \( \angle EOF \) at point \( P \), we specifically want to describe the steps for the construction accurately. The correct sequence of steps should replicate the measurements of the original angle while also ensuring the angles are equivalent.
Based on the options you provided, let's analyze them for correctness:
1. **Step 1**: Draw auxiliary segment \( AB \) and place point \( P \) on the auxiliary segment.
2. **Step 2**: Measure the length of \( \overline{OF} \) using a compass and use that length to place point \( D \) on the auxiliary segment by placing the pointed end of the compass on point \( P \) and drawing an arc.
3. **Step 3**: Measure the length of \( \overline{FE} \) using a compass and use that length to draw another smaller arc above point \( D \) by placing the pointed end of the compass on point \( D \).
4. **Step 4**: Place point \( C \) at the intersection of the two arcs and draw a line connecting points \( P \) and \( C \).
Let's analyze if this option is a possible step for constructing \( \angle CPD \):
- In Step 2, he correctly measures \( \overline{OF} \) and transfers the distance to \( P \).
- In Step 3, measuring \( \overline{FE} \) and drawing an arc above point \( D \) is also consistent with the angle copying process.
- Step 4's instruction to put point \( C \) at the intersection of the arcs and connecting to point \( P \ is also valid.
Therefore, the construction appears correct because it establishes the necessary elements to replicate \( \angle EOF \) at \( P \).
None of the other options accurately reflect this correct construction process. Therefore, the chosen steps are:
**Option 1**:
1. Draw auxiliary segment \( AB \) and place point \( P \) on the auxiliary segment.
2. Measure the length of \( \overline{OF} \) using a compass and use that length to place point \( D \) on the auxiliary segment by placing the pointed end of the compass on point \( P \) and drawing an arc.
3. Measure the length of \( \overline{FE} \) using a compass and use that length to draw another smaller arc above point \( D \) by placing the pointed end of the compass on point \( D \).
4. Place point \( C \) at the intersection of the two arcs and draw a line connecting points \( P \) and \( C \).
Based on the options you provided, let's analyze them for correctness:
1. **Step 1**: Draw auxiliary segment \( AB \) and place point \( P \) on the auxiliary segment.
2. **Step 2**: Measure the length of \( \overline{OF} \) using a compass and use that length to place point \( D \) on the auxiliary segment by placing the pointed end of the compass on point \( P \) and drawing an arc.
3. **Step 3**: Measure the length of \( \overline{FE} \) using a compass and use that length to draw another smaller arc above point \( D \) by placing the pointed end of the compass on point \( D \).
4. **Step 4**: Place point \( C \) at the intersection of the two arcs and draw a line connecting points \( P \) and \( C \).
Let's analyze if this option is a possible step for constructing \( \angle CPD \):
- In Step 2, he correctly measures \( \overline{OF} \) and transfers the distance to \( P \).
- In Step 3, measuring \( \overline{FE} \) and drawing an arc above point \( D \) is also consistent with the angle copying process.
- Step 4's instruction to put point \( C \) at the intersection of the arcs and connecting to point \( P \ is also valid.
Therefore, the construction appears correct because it establishes the necessary elements to replicate \( \angle EOF \) at \( P \).
None of the other options accurately reflect this correct construction process. Therefore, the chosen steps are:
**Option 1**:
1. Draw auxiliary segment \( AB \) and place point \( P \) on the auxiliary segment.
2. Measure the length of \( \overline{OF} \) using a compass and use that length to place point \( D \) on the auxiliary segment by placing the pointed end of the compass on point \( P \) and drawing an arc.
3. Measure the length of \( \overline{FE} \) using a compass and use that length to draw another smaller arc above point \( D \) by placing the pointed end of the compass on point \( D \).
4. Place point \( C \) at the intersection of the two arcs and draw a line connecting points \( P \) and \( C \).