Golden Triangles
Create TRIANGLE 1
-Construct TRIANGLE 1 with 2 angles measuring 72 degrees and one angle measuring 36 degrees. [br]-Make sure to make the sides of TRIANGLE 1 line segments.[br]-Answer the questions below about TRIANGLE 1.
Create TRIANGLE 2
-Create a 36-degree angle counterclockwise about the left-hand base angle.[br]-Use a line to connect B with the point on the side of the 36-degree angle.[br]-Connect vertex B to the point of intersection of the side of the angle and side or original triangle.[br]-Answer questions about TRIANGLE 2.
Create TRIANGLES 3 an 4
-Repeat the process from Creating TRIANGLE 2 by constructing a 36-degree angle, counterclockwise about the left side base vertex.[br]-Make some guesses about TRIANGLES 3 and 4. Write the guesses under the TRIANGLES 3 and 4 section below. [br]-Confirm if your conjectures/guesses were correct. Explain how you did this below, too.
TRIANGLE 1
Write down at least 3 things that you notice about TRIANGLE 1.
TRIANGLE 1
Calculate the ratio of the length of one of the long sides of TRIANGLE 1 to the base length of TRIANGLE 1. [br][br] RT1 =
TRIANGLE 2
Calculate the ratio of the length of one of the long sides of TRIANGLE 2 and the base length of TRIANGLE 2.[br][br]RT2 =
TRIANGLE 2
What do you notice about TRIANGLE 1 and TRIANGLE 2?
Compare the length of the base of TRIANGLE 1 to the length of one of the longer sides of TRIANGLE 2. What do you notice?
TRIANGLES 3 and 4
Write down your conjectures/guesses about TRIANGLES 3 and 4.
How did you confirm or disprove your conjectures?
TRIANGLES 1, 2, 3, 4
Why are these called Golden Triangles?
TRIANGLES 1, 2, 3, 4
Write down three connections the you observe between the work you did with Golden Triangles and the work you with on the Golden Rectangles.