## Day 1 Refresher on types of triangles and triangle congruencies

### Objectives

Review definition of a triangle and the parts of a triangle

Review congruencies and similarities of triangles

### 1) To introduce the unit have the students discuss everything
they already know about triangles. Highlight the key ideas on
the chalkboard or overhead. Have the students use GSP to represent
these ideas to remind them of the capabilities of GSP when discussing
triangles.

### 2) Ensure in their key ideas they have the correct definition
for what a triangle is:

### A three-sided polygon reminding them
that a polygon is a closed figure in a plane that is made up of
segments that intersect only at their endpoints.

### 3) Have the students identify the parts of the triangles

### a) Sides of a Triangle ABC

b) Vertices of a Triangle ABC

c) Angles of a Triangle ABC

### 4) Remind the students of the different classifications of
triangles by their angles

### a) Acute triangle-all the angles of
the triangle are acute (smaller than 90 degrees)

### b) Obtuse triangle-one angle of the
triangle is obtuse (larger than 90 degrees)

### c) Right triangle-one angle of the
triangle is right (exactly 90 degrees)

### d) Equiangular triangle-all angles
of the triangle are equal

### 5) Lastly review the definition of congruence and postulates
for congruent triangles.

### Two triangles are congruent if and only if their corresponding
parts are congruent (equal).

If triangle ABC is congruent triangle DEF then:

### Segment AB is congruent to Segment DE;
Segment BC is congruent to Segment EF, and Segment AC is congruent
to Segment DF

### Also <A is congruent to <D, <B
is congruent to <E, and <C is congruent to <F

Thus,

### a) SSS (Side - Side - Side) - If the sides of one triangle
are congruent to the sides of a second triangle, then the triangles
are congruent.

b) SAS (Side - Included Angle - Side) - If two sides and the
INCLUDED angle of one triangle are congruent to two sides and
the INCLUDED angle of another triangle, then the triangles are
congruent.

c) ASA (Angle - Included Side - Angle) - If two angles and the
INCLUDED side of one triangle are congruent to two angles and
the INCLUDED side of another triangle, then the triangles are
congruent.

d) AAS (Angle - Angle - Side) - If two angles and a NON-INCLUDED
side of one triangle are congruent to the corresponding two angles
and side of a second triangle, the two triangles are congruent.

Hint - Summary - This is a modification of ASA.... because if
you have two corresponding congruent angles, then the third angles
are also congruent. Therefore if you have the information for
ASA... you can find the third angle and solve by AAS. In the
same way if you have the information for AAS... you can find the
thrid angle and solve by ASA. (AAS & ASA are to be used when
the given information lends itself to one method or the other.)