Geometry Broward
Table of Contents
- Constructions
- Square Inscribed in a Circle
- Perpendicular Through a Point on a Line
- Perpendicular Through a Point NOT on a Line
- Construct Parallel Lines (Rhombus Method)
- Triangle Centers
- Circumcenter Construction
- Circumcenter Investigation
- Orthocenter Investigation
- Incenter Investigation
- Centroid Investigation
- Triangle Centers and the Euler Line
Square Inscribed in a Circle
Explore the geometric properties of a square inscribed in a circle.
Summarize the properties of squares, circles, diameters, chords,and how they would relate if the square is inscribed in a circle, before you start your actual construction. [br][br][u]Hint[/u]: If you are not familiar with the steps necessary for inscribing square in a circle construction, you might want to explore the applet below. Just use the buttons of the [i]Navigation[/i][i] Bar[/i] in order to replay the construction steps.
Task
[size=100]Construct a square inscribed within a circle by following the construction steps provided below.[/size]
Construction Steps:
[size=100][size=100][br][table][tr][td][size=100]1.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100]Construct a circle with center [i]A[/i] through [i]B[/i]. (circle c)[/size][/size][/size][/size][/td][td][br][/td][td][size=100]6.[/size][/td][td][size=100][img]data:image/png;base64,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[/img][/size][/td][td][size=100][size=100][size=100][size=100]Construct a circle with the center at point B and radius of f+.5. (circle e)[/size][/size][/size][/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/size][/td][td][size=100][size=100][size=100]Construct segment [i]AB[/i].[/size][/size] (segment f)[br][/size][/td][td][br][/td][td][size=100]7.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100]Construct the intersection points between circles d & e. [br](points D & E)[/size][/size][/size][/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100]Construct line [i]AB[/i]. (line g)[/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100]8.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct line [i]DE[/i]. (line h)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Construct the intersection point between line g and circle c. (point C)[br][/size][/td][td][size=100][br][/size][/td][td]9.[br][/td][td][size=100][size=100][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/size][/size][/size][/td][td][size=100][/size][size=100][size=100][size=100][size=100][size=100][size=100]Construct the intersection points between line h and circle c. [br](points G & F)[/size][/size][/size][/size][/size][/size][br][/td][/tr][tr][td][size=100]5.[/size][/td][td][size=100][img]data:image/png;base64,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[/img][/size][/td][td][size=100]Construct a circle with the center at point C and radius of f+.5. (circle d)[/size][/td][td][br][/td][td][size=100]10.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/size][/td][td][size=100]Draw Quadrilateral BFCG. (poly1)[/size][/td][/tr][/table][/size][/size]
Circumcenter Construction
Explore the construction of the circumcenter and its relationship with the triangle.
Summarize the properties and construction of the circumcenter of a triangle.[br][br][u]Hint[/u]: If you are not familiar with the construction steps necessary, you might want to explore the applet below. Just use the buttons of the [i]Navigation[/i][i] Bar[/i] in order to replay the construction steps.
Task:
Construct the circumcenter of triangle ABC by following the construction steps provided below the blank worksheet.
Construction Steps:
[table][tr][td][size=100]1.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point A [i]and through point B[/i]. (circle d)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100]8.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][i] line GF[/i]. (line i)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][size=100][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point B [i]and through point A[/i]. (circle e)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][/size][br][/size][/td][td][br][/td][td][size=100]9.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point B [i]and through point C[/i]. (circle k)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100][size=100][size=100]3.[/size][/size][/size][/td][td][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct the intersection points between circle d and circle e. [br](point D & point E)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100]10.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point C [i]and through point B[/i]. (circle p)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][size=100][size=100][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/size][/size][/size][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][i] line DE[/i]. (line f)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][br][/size][/td][td][size=100][br][/size][/td][td]11.[br][/td][td][size=100][size=100][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/size][/size][/size][/td][td][size=100][/size][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct the intersection points between circle k and circle p. [br](point I & point H)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][br][/td][/tr][tr][td][size=100]5.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point A [i]and through point C[/i]. (circle g)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100]12[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][i] line IH[/i]. (line J)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][/table][br][table][tr][td][size=100]6.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct a circle centered at point C [i]and through point A[/i]. (circle h)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][br][/size][/td][td][size=100][br][/size][/td][td]13.[br][/td][td][size=100][size=100][size=100][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/size][/size][/size][/td][td][size=100][/size][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][i] the intersection of line f and line i. (point J) [/i][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size] [br][/td][/tr][tr][td][size=100]7.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct the intersection points between circle g and circle h. [br](point G & point F)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100][/size][/td][td][size=100][/size][/td][td][size=100][size=100][/size][/size][/td][/tr][/table]
Question:
Are line DE, line GF, and line IH always concurrent? (Move points A, B, and C to change the triangle and check your answer.)