14-9 Constructions Review. Geometry Period. Constructions Review
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1 Name Geometry Period 14-9 Constructions Review Date Constructions Review Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral triangle- All interior angles measure 60 degrees. Construction looks like: Construct an equilateral triangle GIVEN side length. Construct a perpendicular bisector GIVEN side length. -Measuring side length to make congruent segments. Construct an inscribed Square. -Properties of squares- Diagonals are perpendicular Bisectors. -Diagonal of a square is the diameter of the circle around it. Constructing a Circumscribed circle (or inscribed triangle) -Circumcenter Point of concurrence where 2 perpendicular Bisectors cross -Properties of the circumcenter (Where is it if triangle is acute, right, Obtuse?). Equidistant from vertices. Perpendicular lines through points off and on the line. Construct an Altitude -Create a SEGMENT first, then perpendicular bisector. -Definition of Altitude use construction of perp. line through a point off the line to help you construct an ALTITUDE.
2 Constructing a square with given side length. -Extend a side perpendicular Bisector Measure lengths. Constructing an angle bisector. -Construct a 30 degree angle. -Construct a 45 degree angle. Constructing an inscribed circle. -Properties of Incenter ( Equidistant from sides, formed by angle bisector. -Construct the incenter (center of the circle), construct a line perp. to a side through incenter (radius length-incenter to midpt) Warm Up! The basics: 1. Construct and angle bisector of the following angle: With the video: 2. Construct a line perpendicular to the given segment. With the video:
3 New a video review? Go to this website for step by step videos! or visit the website at
4 1. Construct the midpoint of segment AB. Label it R. Station 1: Constructions Involving Perpendicular Bisectors With Video: 2. Given circle o, construct a square inscribed in this circle. With Video:
5 3. *The circumcenter is used when we want to construct a circumscribed circle around a triangle. *The circumcenter is found by constructing two perpendicular bisectors of a triangle. Inscribe the given triangle in a circle. (Circumscribe a circle around the given triangle). With Video: 4. The diagram shows the construction of the perpendicular bisector of with midpoint C. Which statement is not true? [1] AC = CB [2] [3] AC = 2AB [4] AC + CB = AB Station 2: Constructions Involving Perpendicular Lines 5. Construct a 90-degree angle: no video. How would you construct a 45-degree angle?
6 6. Construct a line perpendicular to XY through point P. With the video: 7. Construct the altitude from A to side BC. With the video: A A B C B C
7 Key Notes: *All sides of regular polygons congruent. Station 3: Regular Polygon Constructions 8. Construct an equilateral triangle inscribed inside a circle. With Video: What is a measure of an exterior angle of a hexagon? What are the angle measures of the interior angles of the equilateral triangle you would construct in question #8? 9. Construct an equilateral triangle using the given segment. With Video:
8 10. Construct a square whose sides are all the same length as GH With Video: 11. Construct a 30 using any construction we ve learned in class. No video. Station 4: Constructions involving angle bisectors
9 12. Construct the incenter of the triangle shown below With video: Station 5: Application Stations 13. On the line provided, construct a line segment that is double the size of GH. Label it BD. No video. 14. On the line provided, construct a line segment that is half the length of a side in square ABCD. Label it LG. No video.
10 15. Construct a line perpendicular to the radius CD and through point D. With video: 16. No video.
11 17. a) Construct a median to side BC. b) Justify how you know that the line/segment you constructed is a median. 18. Construct the center of the circle below: Check for approval
12 19. Triangle DEF is congruent to Triangle D E F;. Construct line of reflection between the two triangles. No video. Hint: we know a line of reflection is also a. 20. Using a compass and straightedge, construct and label triangle ABC, the image of triangle ABC after a dilation with a scale factor of 2 and centered at B. [Leave all construction marks.] No video.
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Name 2-7 Review Geometry Period Unit 2 Constructions Review Date 2-1 Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral
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Constructing a square with given side length. -Extend a side perpendicular Bisector Measure lengths.
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