More Triangle Inequalities

We continued working with inequality relationships among the sides and among the angles in 1 or 2 triangles. Today, the first theorem that the students explored is that the angle in a triangle that is opened the widest is always opposite the longest side of the triangle (and similiarly for the smallest angle & shortest side, and for the middle angle & middle side). This relationship allows for us to organized the sides and the angles of a triangle from least to greatest even if we only know one set of measurements (all of the sides or at least 2 of the angles). This lesson can be found in the textbook as lesson 5.5

The next theorem that we discussed is the Hinge Theorem (found in lesson 5.6). This theorem is applied to two triangles that have 2 sets of congruent sides. Whichever triangle has the longer of the two remaining sides must have an angle opened wider (the HINGE). We call that angle the "included angle" because it is between the two sets of sides that are congruent. This theorem was demonstrated for the students by using the hinge in the classroom door. As the hinge was opened for a wider angle, then the doorway had more open space across the opening.

Homework: Page 287, #4 - 12 even, #28; Page 289, #2 - 6 even, #18; Page 294, #2 - 10 even.

The next test will be on Thursday, December 10th. It will cover all Geometry topics taught through that date. There will be a review session Wednesday, December 9th, at 7:45 in my classroom (4303).

Remember, there are 6 help sessions offered to our IAA students each week:
Monday, 7:45am with Mrs. Bearden in 4210
Tuesday, 7:45am with Mr. Roth in P123
Tuesday, 3:30pm with Ms. Gonding in 4303
Wednesday, 7:45am with Mrs. Bearden in 4210
Thursday, 7:45 am, with Ms. Dufresne in 5207
Thursday, 3:30 pm, with Mrs. Martina in 5202

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Tuesday