Looking For Pythagorus - Investigation 5.2, Analyzing Triangles
HW FOR DAY 1 – ACE #5 (5, 8 & 17) – starts on page 88
HW FOR DAY 2 – ACE #5 (7, 18 & 43) – starts on page 88
You can use the Pytahgorean Theorem to investigate some interesting
properties of an equilateral triangle. One property is that all equilateral
triangles have reflection symmetries.
Triangle ABC is an equilateral triangle. Line AP is a reflection line for triangle
ABC. If you fold an equilateral triangle along the line of reflection you will
find some properties of any equilateral triangle.
What is true about the angle measures in an equilateral triangle?
What is true about the side lengths of an equilateral triangle?
What can you say about the measures of the following angles? Explain.
Angle CAP
Angle BAP
Angle CPA
Angle BPA
What can you say about line segments CP and PB? Explain.
What can you say about triangles ACP and ABP?
Is there a relationship among the lengths of line segments CP, AP, and AC?
Problem 5.2 – Analyzing Triangles
A. Suppose the lengths of the sides of equilateral triangle ABC are 2 units.
Label the following measures:
1. angle CAP
2. angle BAP
3. angle CPA
4. angle BPA
5. length of CP
6. length of PB
7. length of AP
B. Suppose the lengths of the sides of equilateral triangle ABC triangles are 4
units. Label the following measures:
1. angle CAP
2. angle BAP
3. angle CPA
4. angle BPA
5. length of CP
6. length of PB
7. length of AP
C. Thang thinks he has a way of predicting the length of the height AP for
any equilateral triangle. He has drawn the results of Questions A and B in
the diagram below.
1. The triangles look similar. Are they? Explain.
2. What is the length of A2P? What is the length of C2P?
E. Use the figure below:
A. How many right triangles do you see in the figure?
B. Find the perimeter of triangle ABC. Explain your strategy.
C. Find the area of triangle ABC. Explain your strategy.
D. Find the areas of triangle ACD and triangle BCD.