## Triangles

### Important Questions

Q) In the given figure, ∠ CEF = ∠ CFE. F is the midpoint of DC. Prove that . Ans: Manan ji to solve Therefore, …

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 =…