# TRIANGLE-INEQUALITY-THEOREM.pptx

31 May 2023
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### TRIANGLE-INEQUALITY-THEOREM.pptx

• 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.)
• 12. •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
• 14. 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
• 15. 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
• 16. EXAMPLES m<G = 180 - (60 + 69) m<FHG = 180 – 111 = 69 linear pair
• 17. 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
• 18. EXAMPLES FIN D m JKM  2x – 5 = x + 70 x – 5 = 70 x = 75 m< JKM = 2(75) - 5 m< JKM = 150 - 5 m< JKM = 145˚