Thread: How do you show that the six triangles within a regular hexagon are identical?

How do you show that the six triangles within a regular hexagon are identical?

OR

How do you show that the eight triangles within a regular octagon are identical?

http://resources.metapress.com/pdf-preview.axd?code=vwvf5vuvp18x3qn0&size=largest

draw one line across to form the "roof"

/ \
/----\
|\/|
|/\|
----
then down from left diagonal to centre point and draw them all diagonally and it will make a "house of squares " in a pentagon

sorry for diagram tried my best to draw here lol

Draw a circle around the hexagon or octagon and declare point p the center of the circle. Draw lines from all the vertices of the angles through the center to the vertix on the other side. What you have just created are 6 triangles in the hexagon and 8 in octagon. The lines drawn are all radii of the circle and equal. In addition, they create vertical angles which are equal. Thus you can state that the triangles are congruent by side angle side or sas. Congruent means identical.