## Triangles

### Important Questions

Q) E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ ABE ~…

Q) In 𝛥ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that △ 𝐹𝐵𝐷 ∼ △ DEF and △ DEF ∼…

Q) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn…

Q) Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer.Here the largest…

Q) In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Ans: Step 1: It is given that: ∴ by cross multiplying,…

Q) Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord. Ans: Let’s start…

Q) A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped…

Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your…

Q) In the given figure, PQ is tangent to a circle centred at O and ∠BAQ = 30°; show that BP = BQ. Ans: Here, We…

Q) In the given figure, AB, BC, CD and DA are tangents to the circle with centre O forming a quadrilateral ABCD. Show that angle…

Q) In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC…

Q) In ∆ ABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm and EC = 12 cm then,…

Q) In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:(i) Δ ABD ~ Δ CBD(ii)…

Q) Diagonals AC and BD of a trapezium ABCD intersect at O, where AB || DC. If DO/OB = 1/2, then show that AB =…

Q) A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points…

Q) A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC = 15 m.…

Q) If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm,…

Q) In a Δ ABC, D and E are points on the sides AB and AC respectively such that BD = CE. If ∠B =…

Q) ABCD is a trapezium with AB ǁ DC. AC and BD intersect at E. If Δ AED ~ Δ BEC, then prove that AD…

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

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…

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…

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…

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…

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,…

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…

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…

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

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…

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

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…

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…

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…

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…

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…

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

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 =…

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…

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

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

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

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

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)…

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…

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)…

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…

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…

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

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

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