Question

1. if the diagonals of a rhombus are equal l, then prove it is a square

2. if the adjacent sides of a rectangle are equal then prove that it is a square

3. if the diagonals of a parallelogram are equal, prove that it is a rectangle​

Answer 1

Answer:

Step-by-step explanation:

1.ABCD is a rhombus, in which diagonals AC and BD are equal.

We know that diagonals of rhombus bisect each other.

As AC=BD

∴AO=BO=CO=DO

In △AOB,

⇒AO=OB and ∠AOD=90°

∴∠OAB=∠OBA=  

2 90^o =45°

Similarly in △AOD,

⇒∠OAD=∠ODA=45°

∴∠A=∠OAB+∠OAD=45^o +45^o =90°

Similarly,

⇒∠B=∠C=∠D=90°

here, AB=BC=CD=DA

∴ Quadrilateral ABCD is a square.

2.StatementsDB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯∠ABD≅∠BDC∠DBC≅∠ADB△ABD≅△CBDAD¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ABCD is a squareReasonsReflexive property of CongruencyAIA* TheoremSAS** TheoremCPCTC***Definition of Square■

3.teachoo.com/1205/443/Ex-8.1--2---If-diagonals-of-a-parallelogram-are-equal/category/Ex-8.1/