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?
(1 point)
Responses
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 upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper E upper F with bar using a compass and use that length to draw an arc by placing the pointed end at point upper 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 upper C . Step 4: Place point upper C at the intersection of the two arcs and draw a line connecting points upper E and upper 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 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 upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper O upper F with bar using a compass and use that length to place point upper D on the auxiliary segment by placing the pointed end of the compass on point upper P and drawing an arc. Step 3: Measure the length of Modifying above upper F upper E with bar using a compass and use that length to draw another smaller arc above point upper D by placing the pointed end of the compass on point upper D . Step 4: Place point upper C at the intersection of the two arcs and draw a line connecting points upper P and upper 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.
Step 1: Draw auxiliary segment upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper O upper F with bar using a compass and use that length to place point upper D on the auxiliary segment by drawing an arc. Step 3: Place point upper C on the arc constructed. Step 4: Draw a line connecting points upper E and upper 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.
(1 point)
Responses
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 upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper E upper F with bar using a compass and use that length to draw an arc by placing the pointed end at point upper 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 upper C . Step 4: Place point upper C at the intersection of the two arcs and draw a line connecting points upper E and upper 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 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 upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper O upper F with bar using a compass and use that length to place point upper D on the auxiliary segment by placing the pointed end of the compass on point upper P and drawing an arc. Step 3: Measure the length of Modifying above upper F upper E with bar using a compass and use that length to draw another smaller arc above point upper D by placing the pointed end of the compass on point upper D . Step 4: Place point upper C at the intersection of the two arcs and draw a line connecting points upper P and upper 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.
Step 1: Draw auxiliary segment upper A upper B and place point upper P on the auxiliary segment. Step 2: Measure the length of Modifying above upper O upper F with bar using a compass and use that length to place point upper D on the auxiliary segment by drawing an arc. Step 3: Place point upper C on the arc constructed. Step 4: Draw a line connecting points upper E and upper 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.
Answers
GPT-4o mini
To construct an angle \( \angle CPD \) as a copy of \( \angle EOF \), Omar should follow these steps:
**Step 1:** Draw an 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 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 of \( EF \) using the 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 \( C \).
Based on the provided options, the correct sequence of steps matches the last option:
**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 \( C \).
This construction will create angle \( \angle CPD \) as a copy of angle \( \angle EOF \).
**Step 1:** Draw an 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 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 of \( EF \) using the 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 \( C \).
Based on the provided options, the correct sequence of steps matches the last option:
**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 \( C \).
This construction will create angle \( \angle CPD \) as a copy of angle \( \angle EOF \).