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