What is an Isosceles Triangle? A triangle with at least two congruent sides.

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Presentation transcript:

What is an Isosceles Triangle? A triangle with at least two congruent sides

Geogebra Warm-up 1)Open up the file 5.4 Isosceles Triangles.ggb 2)What type of triangle is ABC? 3)With the move tool (first one), move points B and C to create different triangles. Make a conjecture about isosceles triangles as a conditional statement. 4)Find the converse of the conjecture you just made and see if that is true.

Isosceles Triangle Converse 1) Construct an angle with a given measure. 2) Construct a second angle with the same measure using one of the sides of the first angle. 3) Construct a triangle. 4) Construct a circle with the center being the one angle of the triangle that is not one of the original angles you constructed, through one of the angles you constructed first. 5) Is the converse true?

Isosceles Triangle Conjecture If a triangle is isosceles, then its base angles are congruent.

Proof

Isosceles Triangle Converse If a triangle has two congruent angles, then it is an isosceles triangle.

Proof

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Equilateral Triangle An acute isosceles triangle with three Open a new geogebra file and construct one.

Find a function A(s) for the area of an equilateral triangle in terms of the side length.

Prove that if a triangle is equilateral, it is equiangular. The converse is also true.

Altitude – a line segment that starts at the vertex of the triangle and is perpendicular to the base.

Median – a line segment connecting the vertex of a triangle and the midpoint of the opposite segment.

Symmetry Line in an Isosceles Triangle In an isosceles triangle, the bisector of the vertex angle is also the altitude and the median to the base. Proof: