Triangles

Important Questions

Q) In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z,…

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Q) Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil…

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Q) Scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of…

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Q) Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite…

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Q) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that…

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Q) Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P,…

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Q) If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle…

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Q)  In figure, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T…

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Q)  In Fig. AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. Ans: ∵  AD bisects…

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Q) Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height…

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Q)  In the given figure, ∠ CEF = ∠ CFE. F is the midpoint of DC. Prove that . Ans: Step 1: From given conditions:…

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Q) PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and angle of 30 with…

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Q) Find the area of the unshaded region shown in the given figure. Ans: Let’s redraw the diagram: As we can see in the diagram, in…

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Q) With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle…

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Q) ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC…

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Q)  A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10…

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Q) In the given figure, ABCD is a parallelogram. BE bisects CD at M and intersects AC at L. Prove that EL = 2BL. Ans: …

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Q) In the given figure, CD is perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that CF/CD =…

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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…

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Q) In a Δ PQR, N is a point on PR, such that QN is to PR. If PN x NR = QN2, prove that…

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Q) In the given figure, ∠ ADC = ∠ BCA, prove that Δ ACB ~ Δ ADC. Hence find if AC = 8 cm and…

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Q) If AD and PM are medians of triangle ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that AB / PQ =…

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Q) D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC, prove that CA2 = CB.CD…

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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)…

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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…

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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)…

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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…

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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…

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Q) In the given figure, CD and RS are respectively the medians of Δ ABC and Δ PQR. If Δ ABC ~ Δ PQR then…

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Q) PA, QB and RC are each perpendicular to AC. If AP = x, QB = z, RC = Y, AB = a and BC…

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Q) In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC =…

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