1. 4.4.1 Prove Triangles congruent by SAS and HL

2.  The included angle – the angle formed by two given sides of a triangle  Example:  Given AB and BC, the included angle is  B A B C Included Angle Given Sides

3.  The side lengths define a ratio ◦ This ratio is created by the end points and the distance formula ◦ Only one line can be drawn  given a fixed included angle ◦ any triangle formed is congruent Fixed Included Angle Only one Segment can be drawn

4.  SAS:  Given two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. A BC D Example: AC  CA (Symmetric) CB  AD (Given)  ACB   CAD (AIA)  ACB   CAD (SAS)

5.  We have been working with triangles because they play a big role in other shapes  Previous example (slide 4) was a parallelogram which we will study in chapter 8 after we finish triangles  Other examples exist:  Classify this Circumscribed (outside) figure; Prove using SAS this is a regular hexagon: A F B E D C

6.  P. 243  3, 5, 7, 9, 12, 13, 16 -18, 20, 21, 35