Day 6 ­ Isosceles Triangles

1) Review classifications of triangles by sides
2) Identify and use properties of isosceles triangles
3) Link properties to algebra

1) Review with students classifications of triangles by sides

a) Scalene-no sides are congruent

b) Isosceles-at least two sides are congruent

c) Equilateral-all sides are congruent


2) Using either a Graphing Calculator or GSP, have the students construct an isosceles triangle then do some investigating as far as its sides and its angles.

Have the students construct an angle bisector of one of the vertices and continue investigating.


3) Try to guide the students into realizing the results of the following theorems...then provide them with the following theorems.

Thm: If two sides of a triangle are congruent, then the angles opposite those sides are congruent

Thm: The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle.


4) Explain to the students what it means to be a converse of a theorem. Have them explore whether the converse of the first theorem is also true.

Thm: If two angles of a triangle are congruent, then the sides opposite those angles are congruent


5) Reviewing the terms equilateral and equiangular triangles have the students explore those types of triangles with the last theorem...showing that equiangular triangles are equilateral

Thm: A triangle is equilateral if and only if it is equiangular


6) Have the students link the theorems of an isosceles triangle with algebra

Practice Problem: In triangle ABC, <A is congruent to <B, and m<A = 48. If segment AC = 4x and segment CB = 6x - 5, find the m<C, and the measures of segments AC and BC

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