Unit E: Constructions (3.1-3.4, 3.7, 3.8)
□ I can duplicate segments and angles.
□ I will use a compass and straightedge to duplicate and add segments.
□ I will use a compass and straightedge to duplicate and add angles.
□ I will duplicate given segments and angles to form a polygon.
□ I can construct the perpendicular bisector of a segment.
□ I will use a compass and straightedge to construct a perpendicular bisector.
□ I will locate the midpoint of a segment by constructing a perpendicular bisector.
□ I will explain the relationship between a perpendicular bisector and points on the segment.
□ I will construct a median in a triangle.
□ I will construct a midsegment in a triangle.
□ I will recognize a drawing of the construction of a perpendicular bisector, median, and
midsegment.
□ I can construct a perpendicular to a line.
□ I will use a compass and straightedge to construct a perpendicular to a line from a point on or off
the line.
□ I will construct an altitude in a triangle.
□ I will explain the Shortest Distance Conjecture.
□ I will recognize a drawing of the construction of a perpendicular to a line.
□ I can construct an angle bisectors.
□ I will use a compass and straightedge to construct the bisector of an angle.
□ I will explain the relationship between an angle bisector and the sides of the angle.
□ I will recognize a drawing of the construction of an angle bisector.
□ I can construct points of concurrency.
□ I will describe which construction is used to find each point of concurrency.
□ I will construct the incenter of a triangle.
□ I will construct the circumcenter of a triangle.
□ I will construct the orthocenter of a triangle.
□ I will construct the centroid of a triangle.
□ I can use the special properties of points of concurrency.
□ I will circumscribe a circle around a triangle.
□ I will inscribe a circle in a triangle.
□ I will describe the relationship between the incenter and the sides of a triangle.
□ I will describe the relationship between the circumcenter and the vertices of a triangle.
□ I will describe where each point of concurrency lies in an acute, right, and obtuse triangle.
□ I will explain and use the two special properties of the centroid.
Key Vocabulary and Concepts
altitude
compass
angle bisector
concurrent
centroid
construct
circumcenter
duplicate
circumscribed
equidistant
coincide
incenter
inscribed
median
midsegment
orthocenter
perpendicular bisector
point of concurrency
segment bisector
straightedge
Constructions
Duplicating a Segment
Adding/Subtracting Segments
Duplicating an Angle
Adding Angles
Construct a Perpendicular Bisector
Construct a Median
Construct a Midsegment
Construct a Perpendicular to a Line
Construct an Altitude
Construct an Angle Bisector
Construct an Equilateral Triangle
Conjectures
Perpendicular Bisector Conjecture
Converse of the Perpendicular Bisector Conjecture
Shortest Distance Conjecture
Angle Bisector Conjecture
Angle Bisector Concurrency Conjecture
Perpendicular Bisector Concurrency Conjecture
Altitude Concurrency Conjecture
Online Textbook
http://math.kendallhunt.com
Construct Angles of Various Measures
(i.e. 45o, 60o, 30o, 15o, 75o, 105o, etc)
Construct an Isosceles Triangle
Construct the Incenter
Construct the Circumcenter
Construct the Orthocenter
Circumscribe a Circle About a Triangle
Inscribe a Circle Inside a Triangle
Construct the Centroid
Circumcenter Conjecture
Incenter Conjecture
Median Concurrency Conjecture
Centroid Conjecture
Center of Gravity Conjecture
classpass: elliott12
Online Resources
Demonstration of Constructions (animated demonstrations…very helpful!)
http://www.mathsisfun.com/geometry/constructions.html
Basic Geometric Constructions Video: http://www.youtube.com/watch?v=UZjevRGLjTM
Review of Altitudes, Medians, and Angle Bisectors
http://www.cliffsnotes.com/study_guide/Altitudes-Medians-and-Angle-Bisectors.topicArticleId-18851,articleId-18787.html
Orthocenter of a Triangle Video: http://www.youtube.com/watch?v=_XGbDUzBI9Q
Median Properties/Centroid Video: http://www.youtube.com/watch?v=oHsFJuFOIRA&feature=relmfu
Centroid and Orthocenter Video: http://www.youtube.com/watch?v=ulWcVe1-uIk&feature=related
Properties of a Circumcenter
http://www.brightstorm.com/math/geometry/constructions/constructing-the-circumcenter/
Constructing a Circumcenter: http://www.mathopenref.com/constcircumcenter.html
Properties of an Orthocenter:http://www.brightstorm.com/math/geometry/constructions/constructing-the-orthocenter/
Constructing an Orthocenter: http://www.mathopenref.com/constorthocenter.html
Properties of an Incenter: http://www.brightstorm.com/math/geometry/constructions/constructing-the-incenter/
Constructing an Incenter: http://www.mathopenref.com/constincenter.html
Test Yourself on the Points of Concurrency: http://quizlet.com/503201/triangle-points-of-concurrency-flash-cards/
Overview of Points of Concurrency, Circumscribing a Circle, and Inscribing a Circle
http://www.youtube.com/watch?v=uqkQBsEw3o4
Extension Exercises
Euler Line Exploration: pages 191-192 in textbook
Construction of a Pentagon: http://www.kjmaclean.com/Geometry/PentConstruct.html