Day 6 Isosceles Triangles
Objectives:
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