The precise definition of the figure in the image you are describing is "a straight figure that has no thickness and extends infinitely in two opposite directions."
Use the image to answer the question. What is the precise definition of the figure in the image? (1 point) Responses a straight line that always remains the same distance from another line and, therefore, never intersects it a straight line that always remains the same distance from another line and, therefore, never intersects it a part of the circumference of a circle or other curve that measures the distance between two points on a curve a part of the circumference of a circle or other curve that measures the distance between two points on a curve a straight figure that has no thickness and extends infinitely in two opposite directions a straight figure that has no thickness and extends infinitely in two opposite directions a line that intersects another line at a 90-degree angle
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Consider the following statement: A trapezoid is a four-sided figure with one set of parallel lines. Enter 1 if the statement is a conjecture. Enter 2 if the statement is a definition. Enter 3 if the statement is a theorem. (1 point)
The statement "A trapezoid is a four-sided figure with one set of parallel lines" is a definition. Therefore, you should enter 2.
Thuy examines the figure in the image. She needs to determine if NO¯¯¯¯¯¯¯¯ is a copy of PQ¯¯¯¯¯¯¯¯ . What must she do to show that NO¯¯¯¯¯¯¯¯ is a constructed copy of PQ¯¯¯¯¯¯¯¯ ? (1 point) Responses She must measure the distance from point O to point Q using a compass and place the compass on point P to see if point N is the same distance. She must measure the distance from point upper O to point upper Q using a compass and place the compass on point upper P to see if point upper N is the same distance. She must measure the distance from point N to point O using a compass and place the compass on point P to see if point Q is the same distance. She must measure the distance from point upper N to point upper O using a compass and place the compass on point upper P to see if point upper Q is the same distance. She must measure the distance from point M to point Q using a compass and place the compass on point M to see if point O is the same distance. She must measure the distance from point upper M to point upper Q using a compass and place the compass on point upper M to see if point upper O is the same distance. She must measure the distance from point M to point N using a compass and place the compass on point P to see if point M is the same distance. She must measure the distance from point upper M to point upper N using a compass and place the compass on point upper P to see if point upper M is the same distance.
To determine if \( \overline{NO} \) is a constructed copy of \( \overline{PQ} \), Thuy must compare the lengths of the two segments.
The correct response is: She must measure the distance from point O to point Q using a compass and place the compass on point P to see if point N is the same distance.
This ensures that the distance from P to N is the same as the distance from O to Q, confirming whether \( \overline{NO} \) is indeed a copy of \( \overline{PQ} \).
Use the image to answer the question. Lexi started with CD¯¯¯¯¯¯¯¯ on her paper. She folded her paper so that point C was on top of point D . Then, she unfolded her paper and labeled the intersection of the fold and the line segment with point E . She used a straight edge to draw QR←→ at an arbitrary angle through point E . Finally, she drew CR←→ through points C and R and DR←→ through points D and R . Which line segment or line is the segment bisector in this scenario? (1 point) Responses QR←→ Modifying above upper Q upper R with two-way arrow CR←→ Modifying above upper C upper R with two-way arrow DR←→ Modifying above upper D upper R with two-way arrow CD¯¯¯¯¯¯¯¯
In this scenario, Lexi folded her paper so that point C was on top of point D, creating a fold that intersects the line segment \( \overline{CD} \) at point E. This means that the fold represents the perpendicular bisector of the segment \( \overline{CD} \). Since she drew lines \( \overline{CR} \) and \( \overline{DR} \) through points C and D respectively, these lines extend from points on either end of the segment being bisected.
Thus, the correct answer for the segment bisector in this scenario is:
QR←→ Modifying above upper Q upper R with two-way arrow.
This is because the line \( QR \) intersects \( \overline{CD} \) at point E, effectively acting as the bisector.
Use the image to answer the question. What is the construction that needs to be done to make a copy of ∠BAC ? (1 point) Responses Using a compass, measure the length from point A to point C . Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P . Using a compass, measure the length from point upper A to point upper C . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P . Using a straight edge, construct a horizontal line from point P that intersects with the arc to find the middle of the angle. Using a straight edge, construct a horizontal line from point upper P that intersects with the arc to find the middle of the angle. Using a compass, measure the length from point B to point C . Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P . Using a compass, measure the length from point upper B to point upper C . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P . Using a compass, measure the distance from point Q to point B . Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P .
To make a copy of ∠BAC using a compass and straightedge, the most appropriate construction would be:
Using a compass, measure the length from point A to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.
This method accurately reflects the process of copying an angle, where you measure and replicate the distances of the sides of the angle through point Q to create a congruent angle with point P.
Use the image to answer the question. Isha constructed ∠XYZ and needs to double the angle by constructing a copy of the angle using ray YX as one of the sides of the new angle. He has constructed an arc, as appears in the image. What next step must he take to construct a copy of the angle using ray YX ? (1 point) Responses He must measure the distance between point Y and point Z using a compass. He must measure the distance between point upper Y and point upper Z using a compass. He must measure the distance between point X and point Z using a compass. He must measure the distance between point upper X and point upper Z using a compass. He must measure the distance between point Y and the arc using a compass. He must measure the distance between point upper Y and the arc using a compass. He must draw an arc that intersects the larger arc by placing the pointed end on point X .
To construct a copy of the angle ∠XYZ using ray YX as one of the sides of the new angle, the next step Isha must take after drawing the initial arc is:
He must measure the distance between point Y and point Z using a compass.
This measurement allows him to replicate the angle's side by marking that same distance from point Y along the new ray YX. This step is essential to ensure that the new angle is congruent to the original angle.
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