Constructions Review
Practice all constructions AKS 1-3
Table of Contents
- Construct Congruent Segments
- Construct Congruent Segments
- Construct Congruent Angles
- Construct Congruent Angles
- Inscribe Equilateral Triangles
- Construct Equilateral Triangle Inscribed in a Circle
- Inscribe Hexagon
- Construct Hexagon Inscribed in a Circle
- Perpendicular Bisectors
- Construct Perpendicular Bisector (Midpoint)
- Bisect an Angle
- Construct Angle Bisectors
- Construct Parallel Lines
- Construct Parallel Lines
- Construct Perpendicular through a Point
- Construct a Perpendicular Line through a point Not on the line
- Inscribe a Square
- Construct Square Inscribed in a Circle
Construct Congruent Segments
Follow these steps for congruent segment constructions:
1) Using the SEGMENT TOOL, make a segment CD of any length[br]2) Using the COMPASS TOOL, create a circle with radius AB and center point C[br]3) Using the POINT TOOL, mark the intersection of circle C and segment CD[br][br][i]REMEMBER: Congruent circles have the same radius. [i][i]The compass tool measures and preserves the radius. [/i][/i]Therefore, the [i]compass tool can be used to draw congruent segments.[/i][/i]
Construction #1
Construction #2
Construction #3
Bonus!
Construct a segment that is TWICE the length as segment AB
Click the link below to return to the assignment page
[url=https://ggbm.at/PvRc5ZDv]https://ggbm.at/PvRc5ZDv[/url]
Construct Congruent Angles
Directions
Use the tools provided to construct an angle congruent to the given angle[br][br]CONSTRUCTION STEPS:[br]1) Use the POINT TOOL to mark point F anywhere on segment AB[br]2) Use the COMPASS TOOL to create a circle with radius AF and center point A[br]3) Mark point G where circle A intersects segment AC[br]4) Use the COMPASS TOOL to create a circle with radius AF and center point D[br]5) Mark point H where circle D intersects the ray[br]6) Use the COMPASS TOOL to create a circle with radius FG and center point H[br]7) Mark point I where circle D and circle H intersect[br]8) Use the SEGMENT TOOL to draw segment DI
Construction #1
Construction #2
Click link below to return to the assignment page
[url=https://ggbm.at/PvRc5ZDv]https://ggbm.at/PvRc5ZDv[/url]
Construct Equilateral Triangle Inscribed in a Circle
Follow these steps to construct an equilateral triangle inscribed in a circle.
1) Using the POINT TOOL & SEGMENT TOOL, label point C on circle A to create diameter CB. [br]2) Using the COMPASS TOOL, create a circle with radius AB and center point B[br]3) Using the POINT TOOL, mark points D and F where circle A intersects circle B. [br]4) Using the SEGMENT TOOL, draw a segment from point D to point F.[br]5) Using the SEGMENT TOOL, draw a segment from point D to point C. [br][br][i]RESULT: Equilateral triangle DCF inscribed in circle A.[/i]
Construct Equilateral Triangle Inscribed in a Circle
Construct Hexagon Inscribed in a Circle
Follow these steps to construct a hexagon inscribed in a circle.
1.) Create a circle with a radius length AB, centered at B.[br]2.) Where circle A and circle B intersect, label point C.[br]3.) Create another circle with a radius length AC, centered at C. Label intersection point D.[br]4.) Repeat these steps until you have 6 points around circle A.[br]5.) Using Line Segment tool, create a line segment between each point on circle, to create a hexagon[br][br][i]RESULT: Hexagon inscribed in circle A.[/i]
Construct Hexagon Inscribed in a Circle
Construct Perpendicular Bisector (Midpoint)
Follow these steps to construct perpendicular bisectors
1) Using the COMPASS TOOL, create a circle with radius AB and center point A[br]2) Using the COMPASS TOOL, create a circle with radius AB and center point B[br]3) Using the SEGMENT TOOL, draw a segment that connects the intersections of circles A and B[br]4) Using the POINT TOOL, mark point E at the intersection of segments AB and CD[br][br][i]RESULTS: Segment CD is the [b]Perpendicular Bisector [/b]of segment AB[br] Point E is the [b]Midpoint[/b] of segment AB[/i]
Construction #1
Construction #2
Click link below to return to the assignment page
[url=https://ggbm.at/PvRc5ZDv]https://ggbm.at/PvRc5ZDv[/url]
Construct Angle Bisectors
Follow these steps to bisect an angle:
1) Using the POINT TOOL, mark point D on segment AB[br]2) Using the COMPASS TOOL, create a circle with radius AD and center point A[br]3) Using the POINT TOOL, mark point E where circle A intersects segment AC[br]4) Using the COMPASS TOOL, create a circle with the radius DE and center point D[br]2) Using the COMPASS TOOL, create a circle with the radius DE and center point E[br]3) Using the SEGMENT TOOL, draw a segment from point A to the intersection of circles D and E[br][br][i]RESULTS: Segment AF is the [b]Angle Bisector[/b] of angle CAB[/i]
Click the link below to return to the assignment page.
[url=https://ggbm.at/PvRc5ZDv]https://ggbm.at/PvRc5ZDv[/url]
Construct Parallel Lines
Follow these steps to construct parallel lines
1) Using the POINT TOOL, mark point H anywhere on segment FB [i](Hint: FH must be shorter than FG)[/i][br]2) Using the COMPASS TOOL, create a circle with radius FH and center point F[br]3) Using the POINT TOOL, mark point I at the intersection of circle F and segment FG[br]4) Using the COMPASS TOOL, create a circle with radius FH and center point G[br]5) Using the POINT TOOL, mark point J at the intersection of circle G and segment GC[br]6) Using the COMPASS TOOL, create a circle with radius HI and center point J[br]7) Using the LINE TOOL, draw a line that passes through G and the intersection of circles G and J
Construction #2
Construction #3
Click link below to return to the assignment page
[url=https://ggbm.at/PvRc5ZDv]https://ggbm.at/PvRc5ZDv[/url]
Construct a Perpendicular Line through a point Not on the line
Follow these steps to construct a perpendicular line through a point not on the line
1) Using the POINT TOOL, mark point D on segment AB. [br]2) Using the COMPASS TOOL, create a circle with radius CD and center C.[br]3) Using the POINT TOOL, mark point F at the intersection of circle C and segment AB.[br]Next we will create the perpendicular bisector of segment DF. Follow the steps to create below if you don't remember how to construct it.[br]4) Using the COMPASS TOOL, create a circle with radius FD and center F.[br]5) Using the COMPASS TOOL, create a circle with radius FD and center D. [br]6) Using the LINE TOOL, draw a line that passes through C and the intersections of circles F and D.
Construction #1
Construction #2
Construct Square Inscribed in a Circle
Follow these steps to construct a square inscribed in a circle.
1.) Using the line segment tool, create a diameter from B, through center A. Label Point C.[br]2.) Using the Point tool, create a point to the right of center A, before B. Label Point D.[br]3.) Using the Compass tool, create a circle with the radius CD in length, and center at C. Repeat and make a circle with a radius CD in length and center it at B.[br]4.) Where the circles intersect (above and below center A), using the Line tool create a line through the intersections.[br]5.) Where the line intersects Circle A, label the points.[br]6.) Using the Line Segment Tools, connect the Points on circle A to create a square inscribed in a circle. [br][br][i]RESULT: Square inscribed in circle A.[/i]