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In DeltaABC, the bisector AD of /BAC in...

In `DeltaABC`, the bisector `AD` of `/_BAC` intersects `BC` at `D`. Prove that the `DeltaABC` is an isoceles triangle.

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In DeltaABC , the bisector of /_ABC intersects AC at the point P . Prove that CB: BA=CP:PA .

In DeltaABC , AD is the perpendicular bisector of BC (See adjacent figure). Show that DeltaABC is an isosceles triangle in which AB = AC.

In DeltaABC , the bisector AD of A is perpendicular to side BC Show that AB = AC and DeltaABC is isosceles.

In an isoceles triangle ABC, AB = AC and angleBAC=90^(@) , the bisector of angleBAC intersects the side BC at the point D. Prove that (sec angleACD)/(sin angleCAD)="cosec"^(2)angleCAD.

D, E and F are the mid-points of AB, BC and CA of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

In a isosceles triangle ABC , angleB is right angle. Bisector of angleBAC intersect BC at D. Prove that CD^2= 2BD^2 .

In an isosceles right-angled triangle ABC, /_B=90^(@) . The bisector of /_BAC intersects the side BC at the point D. Prove that CD^(2) =2BD^(2)

E is the mid-point of the medium AD of the DeltaABC . Prove that DeltaBED=1/4DeltaABC .

If in a DeltaABC, CD is the angle bisector of the angleABC, then CD is equal to

In DeltaABC , the point at which the bisectors of the angles /_ABC and /_BAC intersect is called the incentre of the triangle.

CALCUTTA BOOK HOUSE-SIMILARITY-Exercise 5.1
  1. If two or more than two triangles be equiangular and the ratios of the...

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  2. If the shapes and sizes of two or more than two triangles be the same,...

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  3. A straight line parallel to any side of any triangle divides other two...

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  4. PQRS is a trapezium of which PS||QR. Its two diagonals PR and QS inter...

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  5. In DeltaABC a straight line parallel to BC intersects the sides AB and...

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  6. The line segments AB and PQ intersect each other at the point C. AP an...

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  7. In DeltaPQR, /QPR=90^(@) and PDbotQR. If PR=8cm and PQ=6cm, then find ...

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  8. In trapezium PQRS, PQ||SR. If PQ=6cm, SR=9cm and QS=15cm and the point...

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  9. In trapezium PQRS, PQ||SR. If PQ=4 units , SR=6units . If the diagona...

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  10. In DeltaPQR, A and B are two such points on PQ and PR respectively tha...

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  11. In the right-angled triangle ABC, /B=90^(@) and the points D and E are...

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  12. PSis perpendicular on the hypotenuse QR of the right-angled triangle P...

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  13. In DeltaPQR, D and E are two such points on the sides PQ and PR that D...

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  14. In DeltaABC, the bisector of /ABC intersects AC at the point P. Prove ...

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  15. In trapezium ABCD, AB and DC are parallel. A straight line parallel to...

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  16. D is any point on the side BC of the DeltaABC. P and Q are the centroi...

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  17. Prove that the line segment obtianed by joining the midpoints of two t...

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  18. In DeltaABC, the bisector AD of /BAC intersects BC at D. Prove that t...

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  19. Write the following sentences true or false: Square and rhombuses are ...

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  20. AB=6.4cm. It is divided internally and externally at the points P and ...

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