Question

Plz.. give the right answer..​

Answer 1

$\huge\star\:\:{\orange{\underline{\red{\mathbf{Answer}}}}}$

$\huge{\underline{\underline{\tt{\purple{Given}}}}}\:$

• O is the midpoint of PQ .

• PS || RQ .

$\huge{\underline{\underline{\tt{\pink{To\:Find}}}}}\:$

• To prove that ∆POS is congruent to ∆ROQ

• To prove that SO = OR

$\huge{\underline{\underline{\tt{\blue{Solution}}}}}\:$

PO = OQ ( Given )

$\implies$ As O is the midpoint of PQ it will divide it into two equal halves hence they are equal

Angle SOP = Angle QOR

$\implies$ As these are vertically opposite angles and vertically opposite angles are equal .

Angle SPO = Angle OQR

$\implies$ Alternate interior angles are equal .

$\huge{\underline{\underline{\tt{\orange{Now}}}}}\:$

$\implies$∆POS is congruent to ∆ROQ

$\implies$By ASA congruency rule ( Angle side Angle )

$\implies$SO = OR

$\implies$By CPCT

$\huge{\underline{\underline{\tt{\green{Concepts}}}}}\:$

What are vertically opposite angles ?

These are the angles that share the same vertex and are formed on the opposite sides . They are always equal .

What are some congruency rules ?

• ASA ( Angle Side Angle )

• SAS ( Side Angle Side )

• SSS ( Side Side Side )

• RHS ( Right angle - Hypotenuse - Side )

What is CPCT ?

The full form of CPCT is Corresponding parts of Congruent Triangle . According to this theorem . If two or more triangles are congruent to each other then their corresponding parts will be equal .