## Monday, December 1, 2014

### Section 7-1: Drawing Triangles (Day 70)

Well, as you can see, I had no problems linking my computer to the Internet. But I am having health problems -- on Sunday I woke up with an upset stomach -- probably for eating too many leftovers from Thanksgiving. Also, I didn't purchase a new printer -- but my old printer/scanner was having paper jams and other problems. This actually started a few days before buying the new computer.

All in all, what this means is that I don't have a worksheet image to scan. But don't worry -- today's lesson is just a follow-up to the pre-Thanksgiving break lesson. The teacher shows the class the triangles they had drawn, and they compare them. Hopefully, they'll begin to conjecture that SSS, SAS, ASA, etc., are true.

The more important lesson is tomorrow's Lesson 7-2. Hopefully both my stomach and my printer will be working better that day.

The one theorem of this lesson is:

Theorem:
If two triangles have two pairs of angles congruent, then the third pair of angles is congruent.

You can probably figure out how to prove this -- if the first two angle measures are x and y, then the third angle measure is 180 - x - y.

According to the text, a lean-to roof is a roof with only one slanted side. Also, the text states the Triangle Inequality to determine whether the SSS condition is even possible. The text gave the Inequality as a postulate in Section 1-9, but we plan on proving it as a theorem in Chapter 13.

After comparing the triangles, here are the exercises that I wanted to assign. They all come from Section 7-1 of the U of Chicago text, "Drawing Triangles." The last review question is a preview of Section 7-2, where we use the Kite Symmetry Theorem to prove SSS. I wanted to include Question 26 from Lesson 7-1 as a bonus question, but that will be too much trouble to write here.

Exercises
1. What is a lean-to roof?

2. State the Triangle Inequality.

3. Draw/construct a triangle with sides of the lengths given here: 3 cm, 4 cm, 5 cm.

4. Two sides of a triangle are 91 cm and 38 cm. Give the possible lengths of the third side.

5. If two angles of a triangle have measures x and y, what is the measure of the third angle?

6. In quadrilateral ABCD, AC bisects angles DAB and DCB. Why are angles B and D congruent?

7. Draw a triangle with angles of measures 110 and 30.

8. Suppose in a triangular sail ABC, angle A has measure 80, AB = 4.5 meters, and AC = 2 meters. So make a scale drawing using centimeters instead of meters as the unit.

Review Exercises:
9. Triangles QZP and KRA are congruent. List six pairs of corresponding parts.

10. State the Kite Symmetry Theorem.