Section 12.1
Congruent Triangles

• Recall, from Chapter 8, that congruence is a property applied to some geometric items (line segments and angles) but not others (points, rays, and lines).
• We now apply the property of congruence to triangles.
• This congruence can be established by determining congruence of certain relative parts (angles or sides) of the triangles in question.
• It is not necessary to verify congruence of all three sides or all three angles, as we shall see shortly.

1. SSS (Side-Side-Side)
2. SAS (Side-Angle-Side)
3. AAS (Angle-Angle-Side)

• In order for a triangle to be a triangle, the lengths of the three sides must satisfy an important requirement.
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• Possible activity: give students three straws of varying lengths. See how many triangle they can construct. Then have the students measure the straws and verify that the lengths do or do not satisfy the Triangle Inequality.

• 1; 2; 8; 12(a), (b); 18; 38 – 42