## 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