Agenda for Friday, Week 1

Loose ends among the congruence criteria

We have proved ASA and SSS from SAS. What about SSA and AAS?

CLASS ACTIVITY. Given the angle and lengths on the handout, how do you construct a triangle using SSA? What is different about this criterion?

What are our axioms?

A lot has remained unsaid about properties of lines and angles. What we are assuming are:

• The ruler axioms for lines
• The protractor axioms for angles
• SAS criterion for triangle congruence

These axioms can be found in Birkhoff and Beatley (with the exception that SAS is given for similar triangles). But we will work with the measurements of distance and angle just as we have in, say, a calculus class using the number line.

HANDOUT: Page from B&B

The Isosceles Triangle Story

CLASS ACTIVITY: Draw Median, Altitude, Angle Bisector, Perpendicular Bisector of side for General Triangle ABC and isosceles triangle.

• Which of these lines or segments always pass through a vertex in any triangle?
• Which of these lines always pass through a midpoint of a side?
• Which of these lines always end at or pass through an interior point of a side of the triangle?