this problem for the warm up:If you answered correctly, you ar
e ready for this question:2. By now it should be 9:30am and we move on to the main lesson of today, which is 4.2 and 4.3.
Please ready page 204 in your textbook. The conjecture on page 205 reads as follows:
"Isosceles Triangle Conjecture:
If a triangle is isosceles, then its base angles are congruent."
Investigation 2 on page shows that the converse is also true (anyone remeber what the word "converse" means? It reverses an if-then statement. For example: If Shifee is in the classroom, then he is running around. The converse would be: If someone is running around the room then it is Shifee. Sometimes the converse is true, sometimes it isn't.)
"Converse of the isosceles Triangle conjecture: If a triangle has two congruent angles, then it is an isosceles triangle."
You should copy these two conjectures into your notebook.
Now the answer to problem 1 on page 206 is 79 degrees. Can you see why? It is because the three angles inside that triangle have to add up to 180, so 22 + the one base angle + the other base angle must equal 180. But the two base angles are congruent. So it amounts to solving for x using your 9th grade algebra: 22 + 2x = 180. So x=79. Now solve problems 2 through 6 on page 206 to 207.
3. The second lesson for today is 4.3, Triangle Inequalities.
Read page 213. Now can you make pictures on geogabra or activesudio that will support the following three conjectures:
Triangle inequality conjecture: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Side-Angle Inequality conjecture: In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
Triangle exterior angles conjecture: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
4. Homework will be problems 1 through 16 on page 216 and 217.
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