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Triangle sum theorem:
The sum of the interior angle measures of a triangle is 180°
Given: ?ABCwith DE??AC¯
Prove: m?1+m?2+m?3=180°
Proof:
| 1. DE??AC¯ | [ Select ] ["Substitution property", "Angle addition postulate", "Alternate interior angles theorem", "Definition of congruent angles", "Given", "Linear pair theorem"] |
| 2. ?1??DBA ?3??EBC | [ Select ] ["Definition of congruent angles", "Angle addition postulate", "Substitution property", "Given", "Alternate interior angles theorem", "Linear pair theorem"] |
| 3. m?1=m?DBA m?3=m?EBC | [ Select ] ["Linear pair theorem", "Given", "Alternate interior angles theorem", "Definition of congruent angles", "Angle addition postulate", "Substitution property"] |
| 4. m?DBA+m?2=m?DBC | [ Select ] ["Angle addition postulate", "Substitution property", "Definition of congruent angles", "Linear pair theorem", "Given", "Alternate interior angles theorem"] |
| 5. m?DBC+m?EBC=180° | [ Select ] ["Linear pair theorem", "Angle addition postulate", "Substitution property", "Definition of congruent angles", "Alternate interior angles theorem", "Given"] |
| 6. m?DBA+m?2+m?EBC=180° m?1+m?2+m?3=180° | [ Select ] ["Linear pair theorem", "Definition of congruent angles", "Alternate interior angles theorem", "Angle addition postulate", "Substitution property", "Given"] |
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