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Geometric Mean of Similar Triangles : The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.![]() ΔABC ~ ΔBDC ~ ΔADB |
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1) ∠ABC= 90 | 1) Given |
2) BD ⊥ AC | 2) Given |
3) ∠BDC = ∠BDA = 900 | 3) By definition of perpendicular |
4) ∠ABD + ∠DBC = 90 | 4) Since ∠ABC = 90 |
5) ∠C + ∠DBC + 90 = 180 | 5) Angle sum property |
6) ∠C + ∠DBC = 90 | 6) By subtraction property |
7) ∠C = ∠ABD | 7) From (4) and (7) |
8) ΔADB ~ Δ BDC | 8) By AA postulate ( from 3 and 7) |
9) ∠ADB = ∠ABC | 9) Each 900 |
10) ∠A = ∠A | 10) Reflexive (common angle) |
11) ΔADB ~ ΔABC | 11) By AA postulate (from 9 and 12) |
12) ∠C = ∠C | 12) Reflexive (common angle ) |
13) ΔBDC ~ ΔABC | 13) By AA postulate ( from 11 and 12) |
14) ΔADB ~ Δ BDC | 14) from (3) and (7) |
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.