Define: Isosceles Triangle
A triangle with AT LEAST two sides congruent.[br]
Drag the vertices of the triangle and observe the angle measurements. What do you notice? Write a conjecture about the base angles of an isosceles triangle.
The base angles of an isosceles triangle are congruent.
[b]Isosceles Triangle Theorems Part 2[/b]
Drag a vertex of the triangle until two of the angles are congruent. What do you notice about the sides of the triangle? Write a conjecture about the congruent angles and the sides opposite them.
If two angles of a triangle are congruent then the sides opposite them are congruent.[br]
[b]Angle Bisector in An Isosceles Triangle[/b]
Triangle [i]CAB[/i] is an isosceles triangle. The base is segment [i]CB[/i] and the legs are segments [i]CA [/i]and [i]BA[/i]. Segment [i]AD [/i]bisects [math]\angle CAB[/math], the vertex angle of the triangle.
Drag a vertex of the traingle. What do you notice about segments [i]CD[/i] and [i]DB[/i]?
What can you conclude that segment [i]AD[/i] does to segment [i]CB?[/i]
Segment [i]AD[/i] bisects segment [i]CB[/i]
What type of angles are [math]\angle CDA[/math] and [math]\angle BDA[/math]?
Write a conjecture that summarizes your findings about the angle bisector, segment [i]AD[/i], of the vertex angle in an isosceles triangle and its base, segment [i]CB[/i].
The angle bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base of the triangle.