Geometry Period Unit 2 Constructions Review

Transcription

1 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 triangle- All interior angles measure 60 degrees. 2-2 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. 2-3 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. 2-4 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. Constructing a square with given side length. -Extend a side perpendicular Bisector Measure lengths.

2 2-6 Constructing an angle bisector. -Construct a 30 degree angle. -Construct a 45 degree angle. Warm Up! The basics: 1. Construct the midpoint of segment AB. Label it R 2. Construct a regular hexagon inscribed in a circle with given center A. What is a measure of an exterior angle of this figure? 3. Construct a 90 degree angle 4. Use the diagram you just created in #3 to construct a 45 degree angle

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4 Constructions Involving Perpendicular bisectors. 1. Given circle o, construct a square inscribed in this circle. a. What will be your first step? b. What do you know about the diagonals of the square that will help you construct it? 2. a) The circumcenter is used when we want to construct a circle around a triangle. b) The circumcenter is found by constructing two of a triangle. 2. Inscribe the given triangle in a circle. (Circumscribe a circle around the given triangle). Explain each step you took.

5 4. The diagram shows the construction of the perpendicular bisector of. Which statement is not true? [1] AC = CB [2] CB = 1 2 AB [3] AC = 2AB [4] AC + CB = AB 5. Construct the altitude from A to side BC. Constructions Involving Perpendicular Lines A B C 6. Construct a line perpendicular to XY through point P.

6 Additional Regular Polygon Constructions 1. What must be true about a polygon for it to be a regular polygon? 2. How is constructing an equilateral triangle inscribed in a circle different from constructing a hexagon inscribed in a circle? 3. Construct an equilateral triangle inscribed inside a circle in the space provided right. 4. What are the angle measures of the interior angles of the equilateral triangle you would construct in question #3? 5. Construct an equilateral triangle using the given segment. Construct a square whose sides are all the same length as GH

7 Constructions involving angle bisectors 1. Construct a 30 using any construction we ve learned in class. 2. Construct a 45 angle using any construction we learned in class. 3. Construct the incenter of the triangle shown below. 4. Bisect the following angle.

8 Application Use your knowledge of constructions to construct the following 1. On the line provided, construct a line segment that is double the size of GH. Label it BD 2. On the line provided, construct a line segment that is half the length of a side in square ABCD. Label it LG. Construct a line perpendicular to the radius CD and through point D

9 9) a) Locate the midpoint of side BC, label it M. b) Extend a segment from A to M

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