Constructing a square with given side length. -Extend a side perpendicular Bisector Measure lengths.

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1 Name Geometry Period Unit 2 Constructions Review 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. 2-7 Review Date Construcoon like. 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 2-5 Constructing an angle bisector. -Construct a 30 degree angle. -Construct a 45 degree angle. 2-6 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 len th-incenter to mid t New a video review? Go to this website for step by step videos! 1 or visit the website at rmu Th b si s 1. Construct e 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 ang e 4. Use the diagram you just cr t in #3 to construct a 45 degree angle c

3 Ovct vicw Ptrect Constructfons Wiyre does it come from? Equilateral Triangle What can we get It? Goo Perpendicular }isectw What can we get It? Who does it cowte from? Inscribed Hexagon the curve of the wat can we get It?

4 Station 1- 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 circle around a triangle. b) The circumcenter is found by constructing two of a triangle. 2. Inscribe the given trian e in a circle. ( circum ribe a circle around the given triangle). COISirvct O vertex cpÿgu

5 4. The diagram shows the construction of the perpendicular bisector of AB Which statement is not true? [1) AC=CB [31 C=2AB [2) CB- I [4) + = AB-WU-C 5. Construct the altitu e from A to side BC. c 6. Construct a line perpendicular to XY through point P. Explain the steps you took to construct the line.

6 Additional Regular Polygon 1. What must be true about a polygon for it to be a regular polygon? sides 2. How is constructing an equilateral triangle inscribed in a circle different from nstructing a n nse:nbed circle? 3. Construct an equilateral triangle inscribed inside a circle. 4. What are the angle measures of the interior angles of the equilateral triangle would construct 5. Construct an equilateral triangle using the given segment. Construct a square whose sides are all the same len has GH

7 Constructions involving angle bisectors 1. Construct a 300 using any construction we've learned in class. 2. Construct a 450 angle using any construction we learned in class. CD-L biscctcly bisector 3. Construct thei nter of the triangle shown below. Nose inc-eh 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 2. On the line provided, construct a line segment that is half the length of a side in square ABCD c Construct a ine perpendicular to the radius CD and through point D c o

9 Triangle is shown below. Using a compass and straightedge, on the line below. construct and 9) label AABC. such that AABC LXYZ. [Leave all construction marks.) 6 a) Locate the midpoint of side BC, label it M. b) ['tend a segment from A to M