![]() In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig.Show that:(i) ABCD is a square(ii) diagonal BD bisects ∠B as well as ∠D. To Prove : (i) A X Y C (i i) AX is parallel to YC (i i i) AXCY is a parallelogram Proof : A B D C and X and Y are the mid-points of the sides AB and DC respectively (i) A X Y C (1 2 of opposite sides of a parallelogram) (i i) a n d A X Y C (i i i) AXCY is a parallelogram (A pair of opposite sides are equal and parallel. ![]() ![]() If AE 4cm, AF 8 cm and AB 12 cm, find the perimeter. E is a point in AD and CE produced meets BA produced at point F. Find the measure of each angle of the parallelogram. The given figure shows a parallelogram ABCD. Since AD BC with BD as transversal, the alternate interior angles are equal. Given ABCD is a parallelogram To prove: AB 2BC. Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. Two opposite angles of a parallelogram are (3 x 2) and (50 x). If AQ intersects DP at S and BQ intersects CP at R, show. ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Calculate certain variables of a parallelogram depending on the inputs provided. Example 6 ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD.Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Show that i) it bisects ∠C also, ii) ABCD is a rhombus. Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Parallelogram Opposite Sides Converse Given AB CD, BC DA Prove ABCD is a parallelogram.If ABCD is a parallelogram where AP and CQ are perpendiculars from vertices A and C on BD, then ΔAPB ≅ ΔCQD using AAS congruency and AP = CQ. NCERT Maths Solutions Class 9 Chapter 8 Exercise 8.1 Question 10 Since we have a parallelogram, therefore we can say: Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent. Video Solution: ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. Any geometric figure compared to itself is congruent to itself so this is why: 4. ☛ Check: NCERT Solutions Class 9 Maths Chapter 8 (ii) By using the result ΔAPB ≅ ΔCQD., we obtain AP = CQ (By CPCT) ∠ABP = ∠CDQ ( Alternate interior angles as AB || CD) ![]() Given: ABCD is a parallelogram and AP ⊥ DB, CQ ⊥ DBĪB = CD (Opposite sides of parallelogram ABCD) Given: ABCD is a quadrilateral with AC and BD are diagonals. Hence, the ratio of the area of △ADM : area of △ANB = 9 : 25.ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. Theorem 8.7 If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. ∴ A M × C D = 45 ⇒ 6 × C D = 45 ⇒ C D = 45 6 ⇒ C D = 15 2 ⇒ C D = 7.5 \therefore AM \times CD = 45 \\ \Rightarrow 6 \times CD = 45 \\ \Rightarrow CD = \dfrac ∴ Area of △ANB Area of △ADM = A N 2 A M 2 ⇒ Area of △ANB Area of △ADM = 1 0 2 6 2 ⇒ Area of △ANB Area of △ADM = 100 36 ⇒ Area of △ANB Area of △ADM = 25 9 (i) Given, AM = 6 cm and AN = 10 cm and area of parallelogram ABCD is 45 cm 2.Īrea of parallelogram = base x height = CD x AM = BC x AN.
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