Related InterviewSolutions

• ADandBEare respectively altitudes oftriangle ABCsuchthatAE=BD.ProvethatAD=BE.
• Prove that the angle between internal bisector ofone base angle and the external bisector of the other base angle of atriangle is equal to one half of the vertical angle.
• If perpendiculars from any point with an angle onits arms are congruent, prove that it lies on the bisector of that angle.
• AD, BEandCF, the altitudes oftriangle ABCare equal. Prove thatABCis an equilateral triangle.
• If the bisector of the exterior vertical angle ofa triangle be parallel to the base. Show that the triangle is isosceles.
• In Figure, `A C=B C ,/_D C A=/_E C B`and `/_D B C=/_E A Cdot`Prove that triangles `D B C`and `E A C`are congruent, and hece `D C=E C`and `B D=A E`
• The sides `B C ,C A`and `A B`of a triangle `A B C ,`are produced in order, forming exterior angles `/_A C D ,/_B A E`and `/_C B F`. Show that `/_A C D+/_B A E+/_C B F=360^0`
• `If`D is the mid-point of the hypotenuse `A C`of a right triangle `A B C`, prove that `B D=1/2A C`.GIVEN : A `A B C`in which `/_B=90^0`and `D`is the mid-point of `A Cdot`TO PROVE : `B D=1/2A C`CONSTRUCTION Produce `B D`to `E`so that `B D=D Edot`Join `E Cdot`
• In an isosceles triangle altitude from the vertexbisects the base.GIVEN : An isosceles triangle `A B C`such that `A B=A C`and an altitude `A D`from `A`on side `B Cdot`TO PROVE : `D`bisects `B C`i.e. `B D=D Cdot`Figure
• If the altitude from one vertex of a trianglebisects the opposite side, then the triangle is isosceles.GIVEN : A `A B C`such that the altitude `A D`from `A`on the opposite side `B C`bisects `B C`i.e., `B D=D Cdot`TO PROVE : `A B=A C`i.e. the triangle `A B C`is isosceles.