Q) In the given figure, Δ ABC and ΔDBC are on the same base BC. If AD intersects BC at O, prove that Ans: Let’s draw perpendicular from points A and D on line BC: In Δ AON and Δ DOM, ∠ AON = ∠ DOM (interior angles) ∠ ANO = ∠ DMO (given that AN and […]
triangles
Q) In a Δ PQR, N is a point on PR, such that QN is to PR. If PN x NR = QN2, prove that ∠ PQR = 900. Ans: Ans: Given that, PN x NR = QN2 Therefore, In Δ PNQ and Δ QNR, ∠ QNP = ∠ RNQ (given that QN is to
Q) In the given figure, ∠ ADC = ∠ BCA, prove that Δ ACB ~ Δ ADC. Hence find if AC = 8 cm and AD = 3 cm. Ans: Ans: In Δ ACB and Δ ADC, ∠ ADC = ∠ BCA (given) ∠ A = ∠ A (common angle) Δ ACB ~ Δ
Q) If AD and PM are medians of triangle ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that AB / PQ = AD / PM. Ans: Given that, Δ ABC ~ Δ PQR, therefore Since AD is median of BC, hence BC = 2BD Similarly, PM is median of QR, hence QR
Q) D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC, prove that CA2 = CB.CD Ans: Let’s draw the diagram with triangle ABC. Let’s compare Δ CBA with Δ CAD ∠ ADC = ∠ BAC (given) ∠ C = ∠ C
Q) Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in LL and AD (produced) in E. Prove that EL = 2BL. Ans: In Δ BMC and Δ EMD, MC = MD (given) ∠ CMB = ∠ EMD (Opposite angles) ∠ MBC = ∠
Q) Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR. Show that Δ ABC ~ Δ PQR. Ans: Given that, In Δ ABC and Δ PQR, Since AD is median of BC, hence BC = 2BD Similarly, PM is
Q) ABCD is a parallelogram. P is a point on side BC and DP when produced meets AB produced at L. Prove that: (i) (ii) (iii) If LP : PD = 2 : 3, then find BP : BC Ans: VIDEO SOLUTION STEP BY STEP SOLUTION (i) Since DC ǁ AB (and AL) Line CB
Q) Sides AB and AC and median AM of a Δ ABC are proportional to sides DE and DF and median DN of another Δ DEF. Show that Δ ABC ~ Δ DEF. Ans: Construction: Extend AM to A’ such that AM = A’M and extend DN to D’ such that DN = D’N Join
Q) In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1:2. If BE = 1.5 cm, then find the length of BC. Ans: Since AD ǁ BC, and EA cuts these lines, ∠DAE = ∠AEB or (∠OEB) Similarly, Line DB cuts these parallel lines, ∠ADB = ∠DBC