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Math
Geometry
Geometry Module 1 FLVS (study guide answers)
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Terms in this set (30)
angle
a figure consisting of two non-collinear rays or segments with a common endpoint
circle
a set of all points in a plane that are a given distance from a point, the center
line
an infinite number of points extending in opposite directions; only one dimension
line segment
a part of a line that has two endpoints
parallel lines
lines in the same plane that never intersect
perpendicular lines
lines that intersect at 90 degree angles
plane
a flat surface that extends infinitely and has no depth
point
a location, has no dimension
ray
part of a line that has one endpoint and continues in one direction infinitely
vertex
the common endpoint of two segments or rays that form a "corner" of an angle
steps to copy an angle using a compass and straightedge
You are given an angle.
Draw a ray with one endpoint. This endpoint will be the vertex of the new angle.
Place the compass on the vertex of the given angle and swing an arc that intersects both rays of the given angle.
Place the compass on the vertex of the new angle and swing an arc similar to the first one you created.
Open the compass to the width of the intersection points of the rays and arc of the given angle.
Place the compass on the intersection point of the ray and arc of the new angle and swing another arc that intersects the first.
Draw a ray through the new vertex and the intersection point of the two rays.
This second ray creates an angle that is congruent to the given one.
angle bisector using compass and straightedge
You are given an angle.
Place the compass on the vertex of the angle.
Swing an arc that intersects both rays of the angle.
Mark the intersection points of the rays and arc.
Place the compass on one of those intersection points and draw an arc inside the angle.
Keeping the compass at the same width, place the compass on the second intersection point and swing an arc that intersects the first. Mark the intersection point of the two arcs and draw a ray from the vertex through this intersection point.
steps to copy a line segment using compass and straightedge
You are given a segment with two endpoints.
Draw a ray with one endpoint.
Open the compass to the width of the given segment.
Place the compass on the ray's endpoint and swing an arc that intersects the ray. The intersection point of the ray and arc is the second endpoint that makes the new line segment congruent to the given one.
segment bisector using compass and straightedge
You are given a segment with two endpoints.
Place the compass on one of the endpoints and open the compass to a distance more than half way across the segment.
Swing an arc on either side of the segment.
Keeping the compass at the same width, place the compass on the other endpoint and swing arcs on either side so that they intersect the first two arcs created.
Mark the intersection points of the arcs and draw a line through those two points. The point where this new line crosses the given segment is the midpoint and divides the segment in half.
parallel lines using compass and straightedge
You are given a line.
Draw another line that intersects the first line.
Place a point on this second line.
Place the compass on the intersection point of the first line and the second line and swing an arc that crosses both lines.
Keeping the compass at the same width, place the compass on the point on the second line and swing an arc similar to the first—making sure you cross through the second line.
Go back to the given line and open the compass to the width of the intersection of the arc and the two lines.
Keeping the compass at the same width, place the compass on the intersection point of the second line and the arc and swing another arc that intersects the first.
Mark the intersection of the two arcs. Draw a line through the point on the second line and the intersection of the arcs, creating a third line which is parallel to the first.
perpendicular lines w/ a point on the line using compass and straightedge
You are given a line and a point on the line.
Place the compass on the point and swing an arc on both sides of this point, making sure to cross the given line on both sides.
Mark the two intersection points of the given line and two arcs.
Place the compass on one of these intersection points. Open the compass to the second intersection point. Draw an arc above the line.
Keeping the compass at the same width, place the compass on the second intersection point and draw another arc above the line. (Make sure that the two arcs intersect.)
Mark the intersection point of the two arcs.
Draw a line through the arc intersection point and the original point on the line. This new line is perpendicular to the given line.
perpendicular lines w/ no point on line using compass and straightedge
You are given a line and a point that is not on the line.
Place the compass on the given point and open it so that the width of the compass is more than the distance from the given point to the given line.
Swing two arcs that intersect the given line.
Mark the two intersection points of the given line and two arcs.
Place the compass on one of these intersection points and draw two arcs, one on either side of the given line.
Keeping the compass at the same width, place the compass on the second intersection point and draw two arcs, one on either side of the line. Make sure that the two arcs on either side of the line intersect one another.
Mark the intersection point of the two arcs on either side of the line.
Draw a line through these two intersection points. This new line is perpendicular to the given line.
equilateral triangle inscribed in a circle using a straightedge and compass
You are given a circle with the center marked.
Draw a radius of the circle using your straightedge.
Keep your compass open to the width of the radius and place it on the point where the radius and circle intersect.
Swing an arc the length of the radius that intersects the circle to the left of the radius originally drawn.
Keeping your compass at the same width, place it on the new intersection point you created in the previous step.
Continue this process until six points of intersection exist on the circle.
Connect together the first, third, and fifth intersection points.
square inscribed in a circle using straightedge and compass
You are given a circle with the center marked.
Draw a diameter of the circle using your straightedge.
Place your compass on one endpoint of the diameter and open it to a width slightly larger than the radius.
Swing two arcs above and below the diameter.
Repeat this process with the other endpoint.
Connect the points of intersection of the arcs that lie above and below the diameter. This should create two perpendicular lines.
Mark the four points of intersection of the perpendicular lines and the circle.
Connect the four points together.
regular hexagon inscribed in a circle using compass and straightedge
You are given a circle with the center marked.
Draw a radius of the circle using your straightedge.
Keep your compass open to the width of the radius and place it on the point where the radius and circle intersect.
Swing an arc the length of the radius that intersects the circle to the left of the radius originally drawn.
Keeping your compass at the same width, place it on the new intersection point you created in the previous step.
Continue this process until six points of intersection exist on the circle.
Connect the six points of intersection together.
copy a line segment on drawing program
Create segment AB.
Draw point C.
Create circle C with the same radius as segment AB.
Draw point D on circle C.
Connect points C and D with a segment.
Segment CD is a copy of segment AB.
copy an angle on drawing programa
Create ray AB.
Create ray AC.
Create ray DE.
Create circle A with the same radius as segment AB.
Mark the point of intersection between circle A and ray AC. Label this point P.
Create circle D with the same radius as segment AB. Mark the point of intersection between circle D and ray DE. Label this point R.
Create circle R with the same radius as the distance between points B and P.
Mark the points of intersection between circle R and circle D.
Label these points S and T.
Create ray DS.
∡RDS is a copy of ∡BAC.
angle bisector on drawing program
Create ray AB.
Create ray AC.
Create point D on segment AB.
Create circle A with radius AD.
Mark the point of intersection between circle A and ray AC. Label this point E.
Create circles D and E with radii equal in length to the distance between points D and C.
Mark the points of intersection between circles D and E. Label these points F and G.
Create line FG.
Line FG bisects ∡BAC.
segment bisector on drawing program
Create segment AB.
Draw point C anywhere on segment AB.
Create circles A and B which will have radii equal in length to either AC or BC, whichever is longer.
Mark the points of intersection between circles A and B. Label these points P and R.
Create line PR.
Line PR bisects segment AB.
parallel lines on drawing program
Create line AB.
Create point C, not on line AB.
Create point D on the opposite side of line AB from point C.
Draw line CD.
Mark the point of intersection between lines AB and CD. Label this point E.
Create circle E with a radius DE.
Create circle C with a radius equal in length to DE.
Mark the points of intersection between circle E and lines AB and CD. Label these points, clockwise starting at the top, P, Q, R, S.
Mark the points of intersection between circle C and line CD. Label these points T and U.
Create circle T with radius equal in length to the distance between P and Q.
Mark the points of intersection between circle T and circle C. Clockwise, label these points V and W.
Draw line CV.
Line CV is parallel to line AB
perpendicular lines with a point on a line on drawing program
Create line AB.
Draw point C on line AB.
Create circle C with radius BC.
Mark the points of intersection between circle C and line AB. Label these points D and E.
Create point F on segment DB.
Create circles D and B which will have radii equal in length to either DF or BF, whichever is longer.
Mark the points of intersection between circles D and B. Label these points P and Q.
Draw line PQ.
Line PQ passes through point C and is perpendicular to line AB.
perpendicular lines with no point on line on drawing program
Create line AB.
Draw point C, not on line AB.
Create point D on the opposite side of line AB from point C.
Create circle C with radius CD.
Mark the points of intersection between circle C and line AB. Label these points E and F.
Create point G on the same side of line AB as point D.
Create circles E and F, which will have radii equal in length to either EG or FG, whichever is longer.
Mark the points of intersection between circles E and F. Label these points P and Q.
Draw line PQ.
Line PQ passes through point C and is perpendicular to line AB.
equilateral triangle inscribed in a circle on a drawing program
Create circle A with point B on circle A.
Draw line AB.
Mark the points of intersection between circle A and line AB. Label these points P and Q.
Create circle Q with radius AQ.
Mark the points of intersection between circle Q and circle A. Label these points R and S.
Draw segments BR, RS, and SB.
Polygon BRS is an equilateral triangle.
square inscribed in a circle on drawing program
Create circle A with point B on circle A.
Draw line AB.
Mark the points of intersection between circle A and line AB. Label these points P and Q.
Create point E anywhere on segment QB.
Create circles Q and B, which will have radii equal in length to either QE or BE, whichever is longer.
Mark the points of intersection between circles Q and B. Label these points R and S.
Draw line RS.
Mark the points of intersection between line RS and circle A. Label these points V and W.
Draw segments BV, VQ, QW, WB.
Polygon BVQW is a square.
regular hexagon inscribed in a circle on drawing program
Create circle A with point B on circle A.
Create circle B with radius AB.
Mark the points of intersection between circles A and B. Label these points C and D.
Create circle C with radius AB.
Mark the points of intersection between circles A and C. Label these points E and F.
Create circle E with radius AB.
Mark the points of intersection between circles A and E. Label these points G and H.
Create circle G with radius AB.
Mark the points of intersection between circles A and G. Label these points I and J.
Draw segments BC, CE, EG, GI, ID.
Polygon BCEGID is a regular hexagon.
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Verified questions
GEOMETRY
A factory that makes bottles knows that, on average, 1.5% of its bottles are defective. Find the probability that in a randomly selected sample of 20 bottles, at least one bottle is defective.
GEOMETRY
M is the midpoint of $$ \overline {JK}. $$ Find the coordinates of K. J(0, 11), M(-3, 2)
GEOMETRY
The segment with endpoints A(4, 2) and B(2, 1) is reflected across the y-axis. The image is reflected across the x-axis. What transformation is equivalent to the composition of these two reflections? Which solution is incorrect? Explain the error. (A) The image of $\overline{AB}$ reflected across the y-axis has endpoints (-2, 1) and (-4, 2). The image of $\overline { A ^ { \prime } B ^ { \prime } }$ reflected across the x-axis has endpoints (-2, -1) and (-4, -2). The reflections are equivalent to a translation along the vector $\langle -6 , - 3 \rangle$. (B) The angle between the x-axis and the y-axis is $90 ^ { \circ }$. Therefore the composition of the two reflections is equivalent to a rotation about the origin by an angle measure of twice $90 ^ { \circ }$, or $180 ^ { \circ }$.
GEOMETRY
A cube has an edge length of 16 units. Draw a diagram of the cube and find its volume and surface area.
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