# Golden Triangles

## Create TRIANGLE 1

-Construct TRIANGLE 1 with 2 angles measuring 72 degrees and one angle measuring 36 degrees.
-Make sure to make the sides of TRIANGLE 1 line segments.
-Answer the questions below about TRIANGLE 1.

## Create TRIANGLE 2

-Create a 36-degree angle counterclockwise about the left-hand base angle.
-Use a line to connect B with the point on the side of the 36-degree angle.
-Connect vertex B to the point of intersection of the side of the angle and side or original triangle.
-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.
-Make some guesses about TRIANGLES 3 and 4. Write the guesses under the TRIANGLES 3 and 4 section below.
-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. 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. 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.