What is the first step in constructing the angle bisector of angle A?

From point A, draw an arc that intersects the sides of the angle at points B and C.

Draw a line segment connecting points B and C.

From points B and C, draw equal arcs that intersect at D.

Carla drew two arcs of the same radius by placing her compass at each endpoint of $$\overline{AB}$$ to produce the picture below. If she connects the two points where the arcs intersect with a straightedge, what must be true about the segment she creates?

It is perpendicular to and bisects $$\overline{AB}$$ .

It is congruent to and perpendicular to $$\overline{AB}$$ .

It is congruent to and bisects $$\overline{AB}$$ .

It is congruent to, perpendicular to, and bisects $$\overline{AB}$$ .

What is the next step in constructing an angle RTS congruent to the given angle BCD with a straightedge and a compass?

Without changing the compasses' width, place the point of the compass on point T and draw an arc there. Label the point where the arc intersects $$\overrightarrow{TS}$$ .

Set the compasses on Y and adjust its width to point X.

Using T as the center and any radius, draw an arc which intersects $$\overrightarrow{TS}$$ . Label the point where the arc intersects $$\overrightarrow{TS}$$ .

Below are the steps for constructing the bisector of a segment using paper folding, but one step is missing. Which statement represents the missing step? I. Draw a segment and name it PQ. II. ____________________________. III. Label the intersection of PQ and the fold point M. Any bisector of PQ will pass through point M.

Fold the paper so that point P coincides with point Q.

Fold points P and Q together so they meet as closely as possible at the center of the segment.

Fold the paper so that the crease created coincides with PQ.

Fold the paper so that point P lies perpendicular to point Q.

The diagram below shows the construction of the center of the circle circumscribed about △ABC. This construction represents how to find the intersection of

the perpendicular bisectors of the sides of △ABC

the medians to the sides of △ABC

the altitudes to the sides of △ABC

Alex needs to bisect $$\angle ABC$$ using a compass and straightedge. He starts by performing the following steps. Step 1: Place the compass on vertex B of the angle. Step 2: Draw an arc that intersects both sides of the angle. Step 3: Label these intersections as point D and point E. Step 4: ________________________________. Step 5: ________________________________. What are the next two steps Alex should take in his construction?

Step 4: Place the compass at point D and draw an arc in the interior of the angle. Step 5: Without adjusting the compass width, place the compass at point E and draw an arc in the interior of the angle that crosses the other arc.

Step 4: Adjust the compass width to be half the distance between point B and point E, and then place the compass on point E and draw an arc in the interior of the angle that crosses the other arc. Step 5: Place the compass at point D and draw an arc in the interior of the angle.

Step 4: Adjust the compass width to be half the distance between point B and point E, and then place the compass on point E and draw an arc on the exterior of the angle. Step 5: Without adjusting the compass width, place the compass at point D and draw an arc on the exterior of the angle that is opposite the other arc.

Step 4: Without adjusting the compass width, place the compass at point D and draw an arc on the exterior of the angle that is opposite the other arc. Step 5: Adjust the compass width to be half the distance between point B and point E, and then place the compass on point E and draw an arc in the interior of the angle that crosses the other arc.

Geometric Constructions EOC Review

9th Grade

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Mathematics

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9th Grade

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Practice Problem

•

Medium

•

CCSS

HSG.CO.C.9, 4.MD.C.6, HSG.C.A.3

Standards-aligned

ALICIA MORHAIM

Used 7+ times

FREE Resource

16 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Given the diagram below. Which pair of points determines the perpendicular bisector of line segment AB?

A. X, W

B. X, Z

C. Y, W

D. Y, Z

Tags

CCSS.HSG.CO.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The drawing shows the partial construction of ____________.

a bisector of a given angle

an angle congruent to a given angle

a bisector of a given line

a perpendicular of a given line at a point on the line

Tags

CCSS.HSG.CO.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following constructions is illustrated?

An angle congruent to a given angle

The bisector of a given angle

The bisector of a given segment

The perpendicular bisector of a given segment

Tags

CCSS.HSG.CO.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A student used a compass and a straightedge to construct CE in △ABC as shown below. Which of the following statements are true?

∠CEA ≅ ∠CEB

∠ACE ≅ ∠BCE

AE ≅ BE

EC ≅ AC

Tags

CCSS.HSG.CO.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which diagram shows the construction of the perpendicular bisector of line segment AB?

Tags

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What construction does the diagram below represent?

Bisecting an angle

Bisecting a segment

Copying an angle

Copying a segment

Tags

CCSS.4.MD.C.6

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Based on the construction shown below, which statement is true?

The construction shows the intersection of the angle bisectors of a triangle which is the center of the inscribed circle.

The construction shows the intersection of the angle bisectors of a triangle which is the center of the circumscribed circle.

The construction shows the intersection of the perpendicular bisectors of the sides of a triangle which is the center of the inscribed circle.

The construction shows the intersection of the perpendicular bisectors of the sides of a triangle which is the center of the circumscribed circle.

Tags

CCSS.HSG.C.A.3

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Geometric Constructions EOC Review

16 questions

Given the diagram below. Which pair of points determines the perpendicular bisector of line segment AB?

The drawing shows the partial construction of ____________.

Which of the following constructions is illustrated?

A student used a compass and a straightedge to construct CE in △ABC as shown below. Which of the following statements are true?

Which diagram shows the construction of the perpendicular bisector of line segment AB?

What construction does the diagram below represent?

Based on the construction shown below, which statement is true?

What is the first step in constructing the angle bisector of angle A?

Listed below, not in order, are the steps for copying ∠A using a compass and a straightedge. Select the option that lists the steps in the correct order.

Listed below, not in order, are the steps for constructing the perpendicular bisector of AB. Select the option that lists the steps in the correct order.

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