Triangle Congruence and Properties

To determine the type of triangle

To calculate the perimeter of triangles

To establish a basis for proving other geometric statements

To find the area of triangles

Symmetric Property

Transitive Property

Reflexive Property

Substitution Property

Angle-Side-Angle

Side-Side-Side

Side-Angle-Side

Angle-Angle-Side

Corresponding Parts of Congruent Triangles are Congruent

Congruent Parts of Corresponding Triangles are Calculated

Congruent Parts of Corresponding Triangles are Congruent

Corresponding Parts of Congruent Triangles are Calculated

It shows that two triangles are congruent

It shows that a segment is equal to itself

It shows that two different segments are equal

It shows that two angles are equal

AM is twice BM

AM is perpendicular to BM

AM is congruent to BM

AM is half of BM

Angle S is congruent to angle R

Line segment RS is congruent to line segment SP

Line segment RT is congruent to line segment PT

Angle R is congruent to angle P

Angle-Side-Angle

Side-Angle-Side

Angle-Angle-Side

Side-Side-Side

ST is equal to RS

ST is perpendicular to RS

ST is parallel to RS

ST bisects angle RSP

A line that divides an angle into two equal parts

A line that is parallel to a segment

A line that is perpendicular to a segment

A line that divides a segment into two equal parts