EDGE Math 8

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Properties of Equality and Congruence

The algebraic properties of inequality can be applied in the following inequalities for segments and angles:

Inequalities for Segments

Line segment AB is greater than line segment CD, denoted by $\bar{A B} > \bar{C D},$ if any only if $A B > C D .$

Line segment AB is less than line segment CD, denoted by $\bar{A B} < \bar{C D},$ if and only if $A B < C D .$

Inequalities for Angles

Angle A is greater than angle B, denoted by $∠ A > ∠ B,$ if and only if $m ∠ A > m ∠ B .$

Angle A is less than angle B, denoted by $∠ A < ∠ B,$ if and only if $m ∠ A < m ∠ B .$

Whole-Part Inequality

If $A C = A B + B C$ and $B C > 0,$ then $A C > A B .$

If $m ∠ A B C = m ∠ A B D + ∠ B D C,$ then $m ∠ A B C > m ∠ A B D .$