Introduction
Properties of Triangles
Task
During this webquest we will be exploring triangle properties involving perpendicular bisectors, angle bisectors, medians, altitudes, and midsegments. You will be using different webpages to watch videos, read articles, interact with software, and make conclusions about each property.
As you work through this webquest, follow along with your packet which will include your own explanations, constructions, and conclusions. You will have 6 days to complete this packet which will be graded as a summative (see the rubric attached).
Process
Page 1: Perpendicular Bisectors and Angle Bisectors
Knowing and Understanding
Browse the following site. Read about perpendicular bisectors and document in your packet 3 characteristics of perpendicular bisectors.
Visit the following site. Write down your own definition for an angle bisector in your packet. Think about possible applications or uses for angle bisectors. Write down a possible application in your packet.
Constructions
Throughout this webquest, you will be asked to make constructions of various elements dealing with triangles. Read this article concerning the definition and importance of consructions. Answer the questions in your packet.
Follow this link for instruction on how to use a compass and straightedge to construct a perpendicular bisector.
Follow this link for instruction on how to use a compass and straightedge to construct an angle bisector.
Page 2: Bisectors of Triangles
Knowing and Understanding
How do you find the center of a triangle? As you will soon find, there are several different centers of a triangle. Browse the following site. Take note the perpendicular bisector theorem. In your packet, define circumcenter and incenter as well as providing detailed diagrams for each. In your definition be sure to state how the point is found.
Applications
In your packet, include a possible application for both the circumcenter and incenter. Be sure to include diagrams. Use the following sites for ideas. Your application must be different from the examples provided.
Who's going to use this in real life?
Journey to the Center of a Triangle
Page 3: Medians and Altitudes of Triangles
Knowing and Understanding
View the following site to explore the medians of triangles. Document your own definition of the median of a triangle. See the list of properties for the medians of a triangle. Pick one property that you believe is the most noteworthy and list it in your packet as well as an explanation as to why you believe it to be the most significant. Note also the term centroid. Make a diagram of the centroid of a triangle in your packet.
From your previous knowledge of triangles, write a definition of the altitude of a triangle. The altitudes of a triangle lead to the discovery of a new special center of a triangle, the orthocenter. Browse the following site to learn about the orthocenter of a triangle. In your packet, give not only a definition and diagram, but also make conclusions about the location of the orthocenter given an acute, right, or obtuse triangle.
Construction
Follow this link for instructions on how to use a compass and straightedge to constuct the median of a triangle.
Follow this link for instructions on how to use a compass and straightedge to construct the altitude of a triangle.
Page 4: Triangle Midsegment Theorem
Knowing and Understanding
Use the following site to learn about the midsegment of a triangle. Document your own definition of a midsegment. Also state the Midsegment Theorem including an example different from the one provided on the site.
Show me the Math
Solve the midsegment problem in your packet. If you are unsure of how to start, watch the video example on the following site.
Construction
Follow this link for instructions on how to use a compass and straightedge to construct the midsegment of a triangle.
Page 5: Triangle Inequality Theorem
Knowing and Understanding
View the following site to learn about the Triangle Inequality Theorem. In your packet, state the theorem. Look back in your notes and review how to find the converse of a theorem. The converse of the Triangle Inequality Theorem is also true. State this theorem in your packet as well. Then summarize the concepts by explaining how you could identify if 3 side lengths make a triangle.
Show me the Math
Solve the problems in your packet concerning the lengths of the sides of triangles.
Page 6: Hinge's Theorem
Knowing and Understanding
Visit the following video as an introduction to the Hinge Theorem and its converse. Note the connection between this theorem and the SAS congruency theorem and document it in your packet. For another article on the Hinge Theorem, visit this site.
The video uses the picture of a door opening to illustrate this theorem. The website uses the picture of an alligator opening his mouth. Think of another way to explain this theorem to someone and include it in your packet.
Show me the Math
Solve the problems included in your packet.
Evaluation
Find the rubric here.
Conclusion
During this webquest we explored several triangle characteristics and drew conclusions concerning their properties. We also make several constructions using a straightedge and compass. Upon completion of this webquest, you now have a satisfactory knowledge of the 4 points of concurrency in triangles.
Credits
See all sites hyperlinked in the process tab.
Teacher Page
This webquest was created by Danica Scharlemann for the Geometry class at Lakes International Languages Academy (LILA).
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