English Medium इयत्ता ९ - CBSE Question Bank Solutions

Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 35º, determine ∠B.

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ (Figure). Show that AC and PQ bisect each other.

In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

In the following figure, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ABC as shown in the following figure. Show that BC = `1/2` QR.

A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

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