Page 2: Third Case of Equality and Justification Methods

The final page covers the third case of triangle equality and provides guidance on proper mathematical justification. It emphasizes the importance of precise reasoning and proof in geometric problems.

Definition: The third case of equality states that two triangles are equal if all their corresponding sides are equal in length.

Example: Triangle ABC and Triangle DEF are shown to be equal when AB=DF, AC=DE, and BC=EF.

Highlight: The page emphasizes proper justification methods using "If-Then" statements and the importance of finding counterexamples when proving triangles are not equal.

Quote: "D'après le 3eme cas d'égalité des triangles, les triangles ABC et DEF sont égaux" (According to the third case of triangle equality, triangles ABC and DEF are equal).

Page 1: Introduction to Equal Triangles and First Two Cases of Equality

This page introduces the fundamental concepts of equal triangles and presents the first two cases of triangle equality. The content explains how two triangles are considered equal when they are superimposable, meaning they have corresponding sides and angles of equal measure.

Definition: Two triangles are equal when they can be superimposed perfectly, having sides and angles that match in pairs.

Vocabulary:

• Homologous vertices: Corresponding corner points of equal triangles
• Homologous angles: Corresponding angles in equal triangles
• Homologous sides: Corresponding sides in equal triangles

Example: The first case of equality demonstrates that two triangles are equal if they share one side of equal length and two adjacent angles of equal measure.

Highlight: The second case of equality states that two triangles are equal if they have one angle of equal measure contained between two pairs of sides of equal length.