# SAT Math: Triangles

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Equilateral Triangle

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## Description and Tags

This is strictly information about triangles and of its properties in order to learn how to manage triangle questions

### 10 Terms

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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