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Side angle side postulate ->If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent by side angle side postulate. |
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1) AB = AC | 1) Given |
2) AD is a bisector | 2) By construction |
3) ∠BAD = ∠CAD | 3) By definition of angle bisector |
4) AD = AD | 4) Reflexive (common side) |
5) ΔABD ≅ ΔACD | 5) SAS Postulate |
6) ∠B = ∠C | 6) CPCTC |
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1) O is the mid point. | 1) Given |
2) AO = OB | 2) By definition of mid point. |
3) ∠AOC = ∠BOD | 3) Vertically opposite angles |
4) CO = OD | 4) By definition of mid point. |
5) ΔAOC ≅ ΔBOD | 5) SAS postulate |
6) AC = BD | 6) CPCTC |
7) ∠CAO = ∠DBO | 7) CPCTC |
8) AC || BD | 8) If alternate interior angles are congruent then the lines are parallel. |
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1) AD = DC | 1) Given |
2) BD = DE | 2) By construction |
3) ∠ADB = ∠CDE | 3) Vertically opposite angles |
4) ΔADB ≅ ΔCDE | 4) By SAS postulate |
5) EC = AB and ∠CED = ∠ABD | 5) CPCTC |
6) CE || AB | 6) If alternate interior angles are congruent then the lines are parallel |
7) ∠ABC + ∠ECB = 180 | 7) Angles formed on the same side of transveral are supplementary. |
8) 90 + ∠ECB = 180 | 8) Since ∠B = 90 given |
9) ∠ECB = 180 -90 = 90 | 9) By subtraction property |
10) AB = EC | 10) From (5) |
11) BC = CB | 11) Reflexive (Common side) |
12) ∠ABC = ∠ECB | 12) Each 900 |
13) ΔABC ≅ ΔECB | 13) SAS postulate |
14) AC = BE | 14) CPCTC |
15) 1/2AC = 1/2BE ⇒ 1/2AC = BD | 15) Multiply by 1/2 but 1/2BE = BD by mid point definition. |
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.