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1

**Equilateral Triangle**

All sides and angles are equal.

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2

**Isosceles Triangle**

Two sides and two angles are equal.

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3

**Scalene Triangle**

All sides and angles are different.

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4

**Acute Triangle**

All angles are less than 90°

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5

**Right Triangle**

One angle is 90°.

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6

**Obtuse Triangle**

One angle is greater than 90°.

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7

Triangle Inequality Theorem

**Definition**: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

**Formulas**:( a + b > c )

( b + c > a )

( a + c > b )

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8

Similar Triangles

**Definition**: Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Key Ratios: In image

**Tests for Similarity**:**AA (Angle-Angle)**: If two angles of one triangle are equal to two angles of another triangle.**SSS (Side-Side-Side)**: If the sides of one triangle are proportional to the sides of another triangle.**SAS (Side-Angle-Side)**: If one angle and the sides including this angle are proportional.

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9

Congruent Triangles

**Definition**: Triangles are congruent if all corresponding sides and angles are equal.

**Tests for Congruence**:**SSS (Side-Side-Side)**: All three sides are equal.**SAS (Side-Angle-Side)**: Two sides and the included angle are equal.**ASA (Angle-Side-Angle)**: Two angles and the included side are equal.**AAS (Angle-Angle-Side)**: Two angles and a non-included side are equal.**HL (Hypotenuse-Leg)**: In right triangles, the hypotenuse and one leg are equal.

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10

Key formulas:

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