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A set of practice questions related to basic geometric constructions, focusing on the steps required to construct congruent segments, perpendicular bisectors, angle bisectors, and congruent angles. Each question is followed by the correct answer, making it a useful resource for students learning or reviewing these fundamental concepts in geometry. It also covers properties of perpendicular bisectors and angle bisectors, enhancing understanding of geometric principles. This resource is ideal for high school students studying geometry.
Typology: Exams
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Given a segment with endpoints A and B, what figure can you construct using the steps below? Step 1: Draw a ray with endpoint C Step 2: Open the compass to the length of line AB Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D. - correct answer ✔✔A congruent segment Given the segment with endpoints A and B, what figure can you construct using the steps below? Step 1: Put the compass point on A and draw a long arc. Be sure the opening is greater than 1/2 AB. Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y. Step 3: Draw line XY. Label the point of intersection of line AB and XY as M, the midpoint of line AB. - correct answer ✔✔A perpendicular bisector Given an angle A, what figure can you construct using the steps below? Step 1: Put the compass point on vertex A. Draw an arc that intersects the sides of ∠A. Label the points of intersection B and C. Step 2: Put the compass point on C and draw an arc. With the same compass setting, draw an arc using point B. Be sure the arcs intersect. Label the point where the two arcs intersect as D. Step 3: Draw ray AD. - correct answer ✔✔an angle bisector Given an angle A, what figure can you construct using the steps below? Step 1: draw a ray with enpoint S. Step 2: with the compass point on vertex A, draw an arc that intersects the sides of ∠A. Label the points of intersection B and C.
Step 3: With the same compass setting, put the compass point on point S. Draw an arc and label its point of intersection with the ray as R. Step 4: Open the compass to the length BC. Keeping the same compass setting, put the compass point on R. Draw an arc to locate point T. Step 5: Draw ray ST. - correct answer ✔✔a congruent angle How is constructing an angle bisector similar to constructing a perpendicular bisector? - correct answer ✔✔Both constructions require that you find the point where two arcs intersect. Given ∠A, how can you construct an angle whose measure is 1/4m∠A? - correct answer ✔✔Construct the angle bisector of ∠A, and then construct the bisector of one of the newly created angles. How many midpoints does the segment have? - correct answer ✔✔one How many bisectors does the segment have? - correct answer ✔✔infinitely many How many lines in the plane are perpendicular bnisectors of the segment? - correct answer ✔✔one Every point on the perpendicular bisector of a segment is - correct answer ✔✔equidistant from the endpoints of that segment.