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In this section we will discuss square and its theorems.A square is a parallelogram through all political parties equal and all angles are 900Square and also its Theorems :Theorem 1 : The diagonals the a square space equal and also perpendicular to each other.Given :
ABCD is a square.Prove the :
AC = BD and also AC ⊥ BD .
Statements Reasons1) ABCD is a square.1) Given2) ad = BC2) properties of square.3) ∠BAD = ∠ABC3) every 900 and also by properties of square.4) abdominal = BA4) reflexive (common side)5) Δ ADB ≅ ΔBCA5) SAS postulate6) AC = BD6) CPCTC7) OB = OD7) as square is a parallelogram so diagonals of parallelogram bisect every other.8) ab = AD8) properties of square.9) AO = AO9) reflex (common side)10) ΔAOB ≅ ΔAOD10) SSS Postulate11)∠AOB = ∠AOD11) CPCTC12)∠AOB + ∠AOD = 18012) These two angles type linear pair and also Linear pair angles space supplementary).13) 2∠AOB = 18013) addition property.14) ∠AOB = 9014) division property.15) AO ⊥ BD⇒ AC ⊥ BD15) an interpretation of perpendicular.Theorem 2 : If the diagonals that a parallelogram are equal and intersect at ideal angles, then the parallelogram is a square.Given :
ABCD is parallel in i beg your pardon AC = BD and also AC ⊥ BD.Prove the :
ABCD is a square.
StatementsReasons1) ABCD is a parallelogram1) Given2) AC = BD and AC ⊥ BD2) Given3) AO = AO3) Reflexive4) ∠AOB = ∠AOD4) every 9005) OB = OD5) nature of parallelogram.6) ΔAOB ≅ ΔAOD6) SAS Postulate7) abdominal muscle = AD7) CPCTC8) abdominal muscle = CD andAD = BC8) properties of parallelogram.9) ab = BC = CD = AD9) from above10) ab = AB10) reflexive (common side)11) advertisement = BC11) properties of parallelogram.12) AC = BD12) Given13) ΔABD ≅ Δ BAC13) SSS Postulate14) ∠DAB = ∠CBA14) CPCTC15)∠DAB + ∠CBA = 18015) inner angles on the exact same side of the transversal.16) 2∠DAB = 18016) enhancement property17) ∠DAB = ∠CBA = 9017) department propertyPracticeHere is a square attracted for you. Answer the adhering to questions top top the communication of square and also its theorems ( m ---> measure up
(i) m∠A = ------- (ii) m∠B = -------- (iii) m∠C = -------b.
(i) seg(AB) = ------- (ii) seg (BC) = -------- (iii) seg (CD) = -------C.
(i) seg(AC) = ------- (ii) seg (BD) = -------- (iii) seg (BO) = -------d.
(i) seg(AO) = ------- (ii) seg (CO) = --------e.
(i)m∠DOA = ------ (ii) m∠AOB = ------ (iii) m∠BOC = ------f.
(i) Is ab || CD (ii) Is BC || ADQuadrilateral• advent to Quadrilateral• varieties of Quadrilateral• nature of Quadrilateral• Parallelogram and also its Theorems• Rectangle and also its Theorems• Square and its Theorems• Rhombus and its Theorems• Trapezoid (Trapezium)and its Theorems• Kite and its Theorems• Mid suggest TheoremHome Page
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