[b][size=150]In this activity we are exploring the SAS Triangle Conditions. Adjust the[br] two lengths for the sides of a triangle and the measure of the included angle(the angle between the sides) by using the sliders [u]and/or[/u] input boxes. [br][/size][/b]
Make side AB a length of 10 (type the length into the input field), Make side AC a length of 10, now make the angle between them 60 degrees. [br][br]What is the length of side BC? [br][br]What are the other two angles?
Make side AB a length of 15 (type the length into the input field), Make side AC a length of 15, now make the angle between them 90 degrees. [br][br]What is the length of side BC? [br][br]What are the other two angles?
Make side AB a length of 15 (type the length into the input field), Make side AC a length of 20, now make the angle between them 90 degrees. [br][br]What is the length of side BC? [br][br]What are the other two angles?
Make side AB a length of 35 (type the length into the input field), Make side AC a length of 21, now make the angle between them 53.1301 degrees. [br][br]What is the length of side BC? [br][br]What are the other two angles?[br][br]Why do you think I set the angle for input to be such a specific value?
1.) Are there any conditions where there is no triangle possible for your [br]chosen measurements? [br][br] If so, what conditions do the measurements have to have in [br]order for a triangle to exist?
When a specific type of triangle exists, then how many different congruence classes [br](different sizes of triangles) do you think would result?[br]
If two triangles exist and they have two corresponding pairs of [br]congruent sides and the angle between the two sides is congruent,[br]do the two triangles have to be congruent?[br][br][br]Explain by writing about the different triangles you created.
What are the segments AC and AB called in relation to the Circles?
What happens in step 10 of the slider? Use terminology that we have used before.
How are the different triangles being created by GeoGebra?
How could you create congruent triangles with a compass and a ruler(straight edge)?