## Exploration 09 - Petal Triangles

First, as you can see in Exploration 5 as well, I generated a script to create a petal triangle, you can also refer to my petal triangle exploration in the GSP file found attached below.

Based upon how our petal triangle was created with perpendicular lines, I can create a series of right triangles and label all congruent angles of the first two triangles above, which I will do below.

And based on our construction of right triangles via perpendicular lines in the construction of a petal triangle, I will continue labelling congruent angles.

So, the following is true based upon the diagrams above:

Angle A = e + f

Angle B = k + m

Angle C = g + h

Angle A’ = k + g

Angle B’ = e + h

Angle C’= f + m

Angle A’’= m + h

Angle B’’= f + g

Angle C’’=e + k

Angle A’’’= e + f

Angle B’’’= k + m

Angle C’’’ = g + h

Therefore, Angle A = Angle A’’’

Angle B = Angle B’’’

Angle C = C’’’

Using AAA, I can therefore say that Triangle ABC is similar to Triangle A’’’B’’’C’’’.

Angle A = e + f

Angle B = k + m

Angle C = g + h

Angle A’ = k + g

Angle B’ = e + h

Angle C’= f + m

Angle A’’= m + h

Angle B’’= f + g

Angle C’’=e + k

Angle A’’’= e + f

Angle B’’’= k + m

Angle C’’’ = g + h

Therefore, Angle A = Angle A’’’

Angle B = Angle B’’’

Angle C = C’’’

Using AAA, I can therefore say that Triangle ABC is similar to Triangle A’’’B’’’C’’’.

petal.gsp | |

File Size: | 18 kb |

File Type: | gsp |