5.12 Triangles in a Circle
- Author:
- Robert Andruskiewicz , Laurent Théry
- Please note the following information from the diagram:
- AB and CD the two chords
- P the intersection of AC and BD
Today we will looking at triangles created by two chords. Move the points to change the shape of the triangles. Make any initial observations here:
Move the points around the circle, you will notice that angles B and C always remain congruent [same]. Why do you think that is? Hint: If you are unsure, watch the video below, then answer this question.
Now that you've made that observation (and watched the video), do you see that same relationship between angle A and angle D (that angle A is congruent to angle D)? Why or why not?
Notes for AA Similarity
Now, move around the points (A,B,C & D) to make different triangles. Can you visibly see the relationship between the two triangles as similar? [same shape but different size]
- A
- B
In your own words, explain why two triangles, drawn like such in the diagram, must be similar [same shape, different size]?
Congruent triangles are triangles that have the same exact shape and size. Do you think these triangles are ever congruent?
- A
- B
Explain your thinking from the previous question.