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If the bisector of the exterior vertical...

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

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To prove that triangle ABC is isosceles given that the bisector of the exterior vertical angle DAC is parallel to the base BC, we can follow these steps: ### Step-by-Step Solution 1. **Identify the Triangle and Angles**: Let triangle ABC be given, where D is a point such that angle DAC is the exterior angle at vertex A. Let AE be the bisector of angle DAC. 2. **Establish the Parallel Condition**: ...
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If the bisector of the vertical angle of a triangle bisects the base of the triangle. then the triangle is isosceles. GIVEN : triangle A B C in which A D is the bisector of angle A meeting B C in D such that B D=DC TO PROVE : triangleA B C is an isosceles triangle.

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

If the median to the base of a triangle is perpendicular to the base then triangle is isosceles.

If the median to the base of a triangle is perpendicular to the base, then triangle is isosceles.

If the bisectors of the base angles of a triangle enclose an angle of 135^0, prove that the triangle is a right triangle.

If the bisectors of the base angles of a triangle enclose an angle of 135^0, prove that the triangle is a right triangle.

Show that the bisector of vertical angle of an isosceles triangle bisects the base at right angles.

In a triangle A B C , if cos A=(sinB)/(2sinC) , show that the triangle is isosceles.

Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle.

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. A D and B E are respectively altitudes of an isosceles triangle A B...

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  2. P Q R is a triangle in which P Q=P R and S is any point on the side P ...

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  3. If the bisector of the exterior vertical angle of a triangle be par...

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  4. Prove that Two right triangles are congruent if the hypotenuse and o...

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  5. AD, BE and CF , the altitudes of triangle ABC are eq...

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  6. A point O is taken inside an equilateral four sided figure A B C D suc...

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  7. In Delta P Q R , if P Q=Q R and L ,M and N are the mid...

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  8. If two isosceles triangles have a common base, prove that the line ...

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  9. Side Side Side(SSS) Congruence : Two triangles are congruent if the th...

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  10. A B C D is a parallelogram, if the two diagonals are equal, find the...

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  11. In a A B C , it is given that A B=A C and the bisectors of /B a...

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  12. A B C is a triangle in which /B =2 /CdotD is a point on B C s...

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  13. In A B C ,\ /A=100^0a n d\ A B=A Cdot Find /B\ a n d\ /C

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  14. In Figure, A B=A C\ a n d\ /A C D=120^0dot Find /A

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  15. Prove that measure of each angle of an equilateral triangle is 60^0...

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  16. In Figure O is the mid-point of A B\ a n d\ C Ddot Prove that \ A O C...

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  17. In Figure, it is given that A B=C F ,\ E F=B D\ a n d\ /A F E=\ /C B...

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  18. In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A...

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  19. In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q...

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  20. In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C o...

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