TRIANGLE-INEQUALITY-THEOREM.pptx

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1. TRIANGLE INEQUALITY THEOREM

2. Theorems on triangle inequalities are categorized into two. These are the inequalities in one triangle and inequalities in two triangles

3. . For inequalities in one triangle the following theorems apply: 1. Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎) 2. Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠) 3. Triangle Inequality Theorem 3 (𝑆1 + 𝑆2 > 𝑆3) 4. Exterior Angle Inequality Theorem.  

4. Inequalities in two triangles Use either of these theorems: 1. Hinge Theorem or SAS Inequality Theorem 2. Converse of Hinge Theorem or SSS Inequality Theorem

5. Example 1 List down the angles of ∆ 𝐺𝑂𝑇 from greatest to least measure. (Note: The figure is not drawn to scale.)

6. When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles . The angles that form linear pairs with the interior angles are the exterior angles . Angles

7. Exterior Angle Theorem An exterior angle of a triangle… … is equal in measure to the sum of the measures of its two remote interior angles . remote interior angles Exterior angle

8. Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles 3 2 1 4 exterior angle remote interior angles m<1 + m<2 = m<4

9. Examples m <G = 180 - (60 + 69) m<FHG = 180 – 111 = 69 linear pair

10. Examples x 82 ° 30 ° y Find x & y x = 68 ° y = 112 ° y = 30 + 82 y = 112˚ 180 = 30 + 82 + x 180 = 112 + x 68˚ = x

11. Examples Find 2x – 5 = x + 70 x – 5 = 70 x = 75 m< JKM = 2(75) - 5 m< JKM = 150 - 5 m< JKM = 145˚