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 […]
triangles
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
Q) In the given figure, CD and RS are respectively the medians of Δ ABC and Δ PQR. If Δ ABC ~ Δ PQR then prove that: (i) Δ ADC ~ Δ PSR (ii) AD x PR = AC x PS Ans: (i) Its given that: CD is median of ΔABC RS is median of ΔPQR ΔABC∼ΔPQR AB =
Q) PA, QB and RC are each perpendicular to AC. If AP = x, QB = z, RC = Y, AB = a and BC = b, then prove that + = Ans: Let’s look at Δ CQB & Δ CPA, By AA similarity theorem, ∠PAC = ∠QBC (perpendicular to AC) ∠PCA = ∠QCB
Q) In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY. Ans: Since XZ ǁ BC, Therefore, (BPT Theorem) ∴ ………….. (i) Since XZ ǁ BC, ∴ XY ǁ BM ∠ AXY = ∠