4.4 Isosceles triangle theorems

Today we learned a theorem and its converse for isosceles triangles. We also learned three corollaries and a theorem about perpendicular bisectors.

Theorem: If 2 sides of a triangle are congruent, then the angles opposite those sides are also congruent.
Converse: If 2 angles of a triangle are congruent, then the sides opposite those angles are also congruent.

Corollary 1: An equilateral triangle is also equiangular.
Corollary 2: An equilateral triangle has 60 degree angles.
Corollary 3: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

This picture has the vertex angle (C), the base (C), the base angles (B and A), and the congruent legs (B and A). Both sets of A and B are congruent, and both Cs can be bisected with a perpendicular bisector.

Isosceles triangle perpendicular bisector: a line that bisects the vertex angle and the base, and is perpendicular to the base.
Perpendicular bisector theorem: If an isosceles triangle has a perpendicular bisector, then it is perpendicular at the midpoint of the base.

Here is a 5 minute video on the isosceles triangle theorems:


http://www.5min.com/Video/How-to-Use-Properties-of-an-Isosceles-Triangle-516909805


And last but not least, the next scribe is...


NOT Matt, Kerry, Katie, Krista, Francis, Ashley, JD, Sean, David, Tim, Emma, Hollee, Zahra, Phill J, or Dmitri. So that leaves...


ALIVIA! MWA-HAHAHAHAHAHAHAHAHAHA! Happy Halloween! Or not! MWA-HA-HA! I'm not feeling too evil, or I would have picked Phill J. That would be EVIL!


PS If the video has an error (which it probably will), then I sent Ms Hunt an email with the video as well. Bye! -Phil K

4.1 Congruence - FRANCIS

*Triangles are congruent when their corresponding angles and sides have the same measure.

*Corresponding- same location, found by vertices, found by common sense

Given: Triangle ABC is congruent to Triangle GEF

Angle A is congruent to angle G, angle B is congruent to angle E, angle C is congruent to angle F

Line ab is congruent to line GE, line BC is congruent to line EF, ac is congruent to line GF

->AB - the distance from A to B, measured in equality

Line AB - line segment AB, can be congruent

NEW INFO! NEW INFO!

- - A shape that is congruent to another shape has the same size

- - If there are no marks on a diagram, then you can’t determine congruency, sometimes because we may have been given a congruency statement