Inscribed equilateral triangle. · 2016/09/02 · Geometry Period Unit 2 Constructions Review 2-1...
Transcript of Inscribed equilateral triangle. · 2016/09/02 · Geometry Period Unit 2 Constructions Review 2-1...
2-7 ReviewName
DateGeometry 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.
2-2 Construct an equilateral triangle GIVEN sidelength.
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.
Construction looks like: Construcoon like.
Construction looks like:
Construction looks like:
Construction looks like:
Construction looks like:
Construction looks like:
-Definition of Altitude* use construction of perp.
line through a point off the line to help you
construct an ALTITUDE. Construction looks like:
Constructing a square with given side length.
-Extend a side perpendicular Bisector
Measure lengths.
2-5 Constructing an angle bisector.-Construct a 30 degree angle.
-Construct a 45 degree angle.
2-6 Constructing an inscribed circle.
Construction looks like:
Construction looks like:
-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 http://www.mathsisfun.com/geometry/constructions.html
rmU Th b si s•
1. Construct e midpoint of segment AB. Label it R
3. Construct a 90 degree ang e
2. Construct a regular hexagon inscribed in a circle with
given center A. What is a measure of an exterior angle of
this figure?
4. Use the diagram you just cr t in #3 to construct a 45 degree angle
c
Ovct•vicw
Ptrect Constructfons
Equilateral Triangle
Perpendicular }isectw
Inscribed Hexagon
Wiyre does it come from?
What can we get It?
Goo
What can we get It?
Who does it cowte from?
the curveof the
wat can we get It?
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
b) The circumcenter is found by constructing two
circle around a triangle.
of a triangle.
2. Inscribe the given trian e in a circle. ( circum ribe a circle around the given triangle).
cpŸGu
COISirvct O
vertex
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.
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
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.
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
Triangle is shown below. Using a compass and straightedge, on the line below. construct and9) 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