1.5 Relationships Within Triangles
Midsegments of a Triangle
Pacing:This lesson should take one class period
Goal:This lesson introduces students to the concept of midsegments and the properties they hold.
Extension:Have students find the other midsegments to the triangle of the introduction
Students will need to measure XY to find its midpoint, call it C, and create two new line segments: ACandBC.
Encourage students to analyze the three midsegments. What do the segments form? What relationships can be seen?
The midsegments form a second triangle.ABis parallel toXY,ACis parallel toZY,andBCis parallel toX Z.
Discuss the proof of the first section of the Midsegment Theorem with your class. It may be helpful to begin with
the figure above, and with each new justification, add it to the drawing.
Extension!Have your students take the paragraph proof of the Midsegment Theorem and rewrite it into 2-column
form.
Additional Example:Findx, and the lengths ofDEandBC.
Perpendicular Bisectors in Triangles
Pacing:This lesson should take one class period
Goal:Students are introduced to the concept of thecircumcenter of a triangle.The process of finding the circum-
center uses perpendicular bisectors, which students can either draw using a protractor or construct using the method
found in theUsing Congruent Triangleslesson.
1.5. Relationships Within Triangles