Topics Covered

9 key topics in this chapter

Congruence of Triangles

SAS Congruence Rule

ASA Congruence Rule

AAS Congruence Rule

SSS Congruence Rule

RHS Congruence Rule

Properties of Isosceles Triangles

Inequalities in Triangles

Angle-Side Relationships

Study Resources

Formula / Rule	Expression
SAS Congruence	\(\text{Two sides & included ∠ of} △ABC = △DEF\)
ASA Congruence	\(\text{Two ∠s & included side}\)
AAS Congruence	\(\text{Two ∠s & non-included side}\)
SSS Congruence	\(\text{All three sides equal}\)
RHS Congruence	\(\text{90°, hypotenuse, one side (right △s only)} \)
Isosceles △ Thm	\(AB = AC ⟹ ∠B = ∠C\)
Converse	\(∠B = ∠C ⟹ AB = AC\)
Inequality	\(AB > AC ⟺ ∠C > ∠B\)

SAS: two sides and the included angle. ASA: two angles and the included side. AAS: two angles and a non-included side.

SSS: all three sides. RHS: right angle, hypotenuse, and one side — only for right-angled triangles.

Angles opposite equal sides are equal (isosceles triangle theorem). Conversely, equal angles imply equal opposite sides.

In a triangle, the side opposite the greater angle is longer. Conversely, the angle opposite the longer side is greater.