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In an isosceles triangle ABC, with AB =A...

In an isosceles triangle ABC, with AB =AC, the bisectors of `angleB` and `angleC` intersect each other at 'O'. Join A to O. AO bisects `angleA`

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In an isosceles triangle ABC, with AB=AC, the bisectors of /_B and /_C intersect each other at O. Join A to O. Show that: OB=OC

In an isosceles triangle ABC, with AB = AC, the bisectors of /_ B and /_ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects /_A

Knowledge Check

  • The inverse of "if in a triangle ABC, AB = AC then angleB = angleC " is

    A
    If in a triangle ABC, `angleB = angleC` then AB = AC
    B
    If in a triangle ABC, `AB != AC`, then `angleB != angle C`
    C
    If in a triangle ABC, `angleB != angleC`, then `AB != AC`
    D
    If in a triangle ABC, `angleB != angleC`, then `AB = AC`

  • The converse of "if in a triangle ABC, AB = AC then angleB = angle C " is

    A
    If in a triangle ABC, `angleB = angleC` then AB = AC
    B
    If in a triangle ABC, `AB != AC`, then `angleB != angle C`
    C
    If in a triangle ABC, `angleB != angleC`, then `AB != AC`
    D
    If in a triangle ABC, `angleB != angleC`, then `AB = AC`

  • The contrapositive of "if in a triangle ABC, AB = AC then angleB = angleC " is

    A
    If in a triangle ABC, `angleB = angleC` then AB = AC
    B
    If in a triangle ABC, `AB != AC`, then `angleB != angle C`
    C
    If in a triangle ABC, `angleB != angleC`, then `AB != AC`
    D
    If in a triangle ABC, `angleB != angleC`, then `AB = AC`

    • Similar Questions

    Explore conceptually related problems

    In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

    ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD "||" BA as shown in the figure. Show that (i) angleDAC = angleBCA (ii) ABCD is a parallelogram

    If a quadrilateral ABCD, the bisector of angleC angleD intersect at O. Prove that angleCOD=(1)/(2)(angleA+angleB)

    The inverse of "if in a triangle ABC, AB gt AC then angleC gt angleB " is

    The converse of "if in a triangle ABC, AB gt AC then angleC gt angleB " is

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