Q3 of 35 Page 69

Diagonals of a square IJKL intersects at point M, Find the measures of ∠IMJ, ∠JIK and ∠LJK.

The given quadrilateral is a square

⇒ all the angles are 90°


∴ ∠JIK = 90°


Since the diagonals are to each other ∠IMJ = 90°


Since the diagonals os a square are bisectors of the angles also


∠LJK = ∠IJL = 1/2 × 90° = 45°


More from this chapter

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1

Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD = 35° then find ∠ACB.

 2

In a rhombus PQRS if PQ = 7.5 then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.

 4

Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

 5

State with reasons whether the following statements are ‘true’ or ‘false’.

(i) Every parallelogram is a rhombus.


(ii) Every rhombus is a rectangle.


(iii) Every rectangle is a parallelogram.


(iv) Every square is a rectangle.


(v) Every square is a rhombus.


(vi)Every parallelogram is a rectangle.