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​Welcome to Grade 8 Mathematics

​with sir RJ

Triangle Inequality Theorems

Open Ended

What are the different types of triangles that you know?

Inequalities in One Triangle

:)

Triangle Inequality Theorem 1 (𝑺𝒔→𝑨𝒂)

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Triangle Inequality Theorem 2 (𝑨𝒂→𝑺𝒔)

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

Triangle Inequality Theorem 3 (𝑺𝟏+𝑺𝟐>𝑺𝟑)

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

Multiple Choice

Which of the following measurements can be used to be able to construct a triangle?

• 10cm, 5cm, 4cm

• 6cm, 7cm, 9cm

• 11cm, 7cm, 4cm

• 3cm, 4cm, 5cm

Inequalities in Two Triangles

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Hinge Theorem or SAS Inequality Theorem

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.

Converse of the Hinge Theorem or SSS Inequality Theorem

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, Then the included angle of the first triangle is larger than the included angle of the second.