Virat

Asked: September 30, 2026In: Class 9 Maths

(i) If P, Q, R are the midpoints of sides AB, AC, BC respectively of △ABC, show that △PQR is congruent to △QPA and to two other triangles which you should identify. (ii) Suppose someone erases △ABC, leaving only △PQR on the paper. Can you reconstruct △ABC from △PQR?

(i) By the Midpoint Theorem, PQ = BC/2 = BR = RC, QR = AB/2 = AP = PB and PR = AC/2 = AQ = QC, so △PQR ≅ △QPA ≅ △RPB ≅ △CQR by SSS. (ii) Yes, construct ...

Virat

Asked: September 30, 2026In: Class 9 Maths

Let ABCD be a parallelogram with AB ≠ BC. Show that the pairwise intersection points of the four angle bisectors form the vertices of a rectangle (see Fig. 12.11). Why did we assume AB ≠ BC?

Adjacent angles of a parallelogram sum to 180°, so their bisectors add to 90°, forcing right angles at intersections to form a rectangle. If AB = BC, all bisectors intersect at a single point. Cbse Class 9 Maths Ganita Manjari Part ...

Virat

Asked: September 30, 2026In: Class 9 Maths

The following questions examine converses of true properties. Answer them with Yes or No. If your answer is No, what extra condition can you add so that the answer becomes Yes? (i) If the diagonals of a quadrilateral ABCD bisect its angles, must ABCD be a rhombus? (ii) If the diagonals of a quadrilateral ABCD bisect each other at right angles, must ABCD be a rhombus? (iii) If the diagonals of a quadrilateral ABCD are of equal length, must ABCD be a rectangle?

(i) Yes. (ii) Yes. (iii) No; an isosceles trapezium also has equal diagonals. Extra condition: the quadrilateral must be a parallelogram or its diagonals must also bisect each other. Ganita Manjari Part 2 chapter 12 question answer Quadrilaterals Solutions – Ganita ...

Virat

Asked: September 30, 2026In: Class 9 Maths

The diagonal AC of a parallelogram ABCD bisects ∠A. Show that it also bisects ∠C and that ABCD is a rhombus.

Since AB ∥ CD and AD ∥ BC, alternate angles are equal. Because AC bisects ∠A, adjacent angles match, proving AC bisects ∠C. In △ABC, equal base angles imply AB = BC, making all sides equal. Cbse released Class 9 Ganita ...

Virat

Asked: September 30, 2026In: Class 9 Maths

(i) A parallelogram with a right angle is a rectangle. (ii) A rhombus with perpendicular diagonals is a square. (iii) If the diagonals of a parallelogram are equal, then it is a rectangle.

(i) True: Adjacent angles sum to 180°, making every angle 90°. (ii) False: Every rhombus has perpendicular diagonals; it needs a right angle to be a square. (iii) True: Equal diagonals in a parallelogram ensure four right angles. Cbse Class 9 ...

Virat

(i) If P, Q, R are the midpoints of sides AB, AC, BC respectively of △ABC, show that △PQR is congruent to △QPA and to two other triangles which you should identify. (ii) Suppose someone erases △ABC, leaving only △PQR on the paper. Can you reconstruct △ABC from △PQR?

Let ABCD be a parallelogram with AB ≠ BC. Show that the pairwise intersection points of the four angle bisectors form the vertices of a rectangle (see Fig. 12.11). Why did we assume AB ≠ BC?

The diagonal AC of a parallelogram ABCD bisects ∠A. Show that it also bisects ∠C and that ABCD is a rhombus.

(i) A parallelogram with a right angle is a rectangle. (ii) A rhombus with perpendicular diagonals is a square. (iii) If the diagonals of a parallelogram are equal, then it is a rectangle.

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