Discussion Forum

Virat

Asked: October 3, 2026In: Class 9 Maths

Suppose P is a point on side AB of △ABC and the line through P parallel to BC meets AC in point Q. For parts (i) to (iii), assume AP = 1, AQ = √5 and see Fig. 12.39. (i) If PB = 2 find QC. (Hint: See the dotted line) (ii) If PB = 1/3 find QC. (Hint: See the dotted lines) (iii) If PB = 2/3 find QC. (Hint: Divide both PB and AP suitably.) (iv) Show that if AP/PB is a rational number, then AP/PB = AQ/QC. In Grade 10, you will prove this equality without assuming AP/PB is rational. That will require a new idea.

(i) QC = 2√5. (ii) QC = √5/3. (iii) QC = 2√5/3. (iv) Dividing AP and PB into equal units and drawing parallels produces congruent intercepts on AC, yielding AP/PB = m/n = AQ/QC. Class 9 maths ganita manjari part 2 ...

Virat

Asked: October 3, 2026In: Class 9 Maths

Consider 4 points A, B, C, D in the plane with no three collinear. Answer the following questions. Some answers may require you to consider different cases, depending on how the points are positioned in the plane. (i) How many different quadrilaterals do they form if the quadrilateral is allowed to be self-intersecting or non-convex? (ii) How many of these quadrilaterals are self-intersecting? How many are convex?

(i) Exactly 3 distinct cyclic edge orderings can be formed. (ii) If the 4 points form a convex hull: 1 is convex and 2 are self-intersecting. If 1 point is inside: 0 are convex, 3 are non-convex and 0 self-intersect. Class ...

Virat

Asked: October 3, 2026In: Class 9 Maths

ABCD is a trapezium with parallel sides AD = 3 cm and BC = 5 cm. E and F are the midpoints of the non-parallel sides. Find the ratio of the areas of the 4-gons AEFD and EBCF.

The segment EF connecting midpoints equals (3 + 5)/2 = 4 cm and is parallel to the bases. Since E and F bisect the non-parallel sides, both resulting trapeziums share identical heights. Hence, their area ratio is (3 + 4)/(4 ...

Virat

Asked: October 3, 2026In: Class 9 Maths

The diagonals AC and BD of a parallelogram ABCD intersect at O. A line through O meets AB and CD at points P and Q respectively. Show that O is the midpoint of PQ. (Multiple proofs are possible. Which is the simplest?)

In triangle OBP and triangle ODQ, OB = OD, ∠POB = ∠QOD and alternate interior angles ∠OBP = ∠ODQ. By ASA congruence, triangle OBP ≅ triangle ODQ, proving OP = OQ; this direct triangle congruence is simplest. Cbse Class 9 Maths ...

Virat

Asked: October 3, 2026In: Class 9 Maths

A more general midpoint theorem and its converse. In a quadrilateral ABCD, suppose AB ∥ DC. Recall that such ABCD is called a trapezium. Let E be the midpoint of AD. A line drawn through E intersects side BC at F. (i) If EF ∥ AB, then show that F is the midpoint of BC. Conclude that EF = (AB + CD)/2. (ii) If F is the midpoint of BC, then show that EF ∥ AB. There are at least two ways to solve (ii). Do it directly by using the midpoint M of BD and showing that EM and FM are the same lines. Or use (i) along with the same idea used in the second proof of the converse of the Midpoint Theorem. Which way do you think is simpler?

(i) Diagonal BD meets EF at M. By Theorem 7, M and F bisect BD and BC. Adding segment lengths gives EF = (AB + CD)/2. (ii) Both methods work; using parallel line uniqueness is simpler. Class 9 Ganita Manjari Part ...

ABCD is a trapezium with parallel sides AD = 3 cm and BC = 5 cm. E and F are the midpoints of the non-parallel sides. Find the ratio of the areas of the 4-gons AEFD and EBCF.

The diagonals AC and BD of a parallelogram ABCD intersect at O. A line through O meets AB and CD at points P and Q respectively. Show that O is the midpoint of PQ. (Multiple proofs are possible. Which is the simplest?)

Which is the best website providing NCERT Solutions?

NCERT Books

Where can I get NCERT books in PDF format?

How to learn palmistry online free in hindi?

Palmistry: Hasth rekha kaise dekhe?

Forgot Password

Discussion Forum Latest Questions