November Challenge

This one also comes from Nathan on the Geometry Math Team...


Prove that the LARGEST ANGLE of ANY TRIANGLE is ALWAYS GREATER THAN OR EQUAL TO 60 degrees.


I would recommend solving it by indirect proof.  Start by saying "What if the largest angle is less than 60? ...

	Chapter 4 Extra Credit Challange!

An art student wants to make a painting with a simple geometric pattern. She starts with a square. She divides this square into two congruent triangles. Then she divides each of these triangles into two smaller congruent triangles. She repeats the process seven more times. What does her pattern look like in the end?

1.  Show that the two triangles are congruent using the Hypotenuse-Leg Theorem.

2.  Use your knowledge of the Hypotenuse-Leg Theorem to divide each triangle in the figure above into two smaller congruent triangles. Repeat the process six more times.

3.  How do you know that the triangles at each step are congruent?

4.  How many triangles of the smallest size are shown?

5.  How many triangles are shown if they each contain 64 of the smallest-sized unit?

6.  How many triangles are shown if they each contain nine of the smallest-sized unit?