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Stay Home , Stay Safe and keep learning!!!HL Postulate(Hypotenuse - Leg) or RHS theorem -> If any two right angles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
|1) AB = GE||1) Construction|
|2) ∠B = ∠FEG||2) Each 900|
|3) BC = EF||3) Given|
|4) ΔABC ≅ ΔGEF||4) By SAS postulate|
|5) ∠A = ∠G||5) CPCTC|
|6) AC = GF||6) If the two angles are congruent then angle opposite to them are equal|
|7) AC = DF||7) Given|
|8) DF = GF||8) By transitive property|
|9) ∠D = ∠G||9) Angles opposite to equal sides in ΔDGF are equal|
|10) ∠A = ∠D||10) From (5) and (9)|
|11) ∠B = ∠E||11) Given|
|12)∠A+∠B=∠D+∠E||12) Adding (10) and (11)|
|13) ∠C = ∠F|| 13) ∠A + ∠B + ∠C = 180
and ∠D + ∠E + ∠F = 1800
|14) ΔABC ≅ ΔDEF||14) By SAS postulate and from (3) (7) and (13)|
|1) QM = MR||1) Given|
|2) LM = MN||2) Given|
|3)ML ⊥ PQ||3) Given|
|4) ∠QLM = 900||4) By definition of perpendicular|
|5) MN ⊥ PR||5) Given|
|6) ∠MNR = 900||6) By definition of perpendicular|
|7) ∠QLM = ∠MNR||7) Each 900|
|8) ΔQLM ≅ ΔRNM||8) RHS theorem|
|9) ∠Q = ∠R||9) CPCTC|
|10) PR = PQ|| 10) If two angles are equal then
side opposite to them are also equal
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