in the adjoining figure abc is a triangle in which ad is the bisector of angle a. if ad perpendicular to bc, show thar triangle abc is isosceles
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In triangle ABD and triangle ACD,
AD = AD (Common)
angle BAD = angle CAD (given, AD is bisector of angle A)
angle ADB = angle ADC (given, AD is perpendicular to BC)
By SAS,
triangle ABD congruent triangle ACD
By CPCT,
AB = AC
angle ABD = angle ACD
or in an isosceles triangle, opposite sides of a triangle are equal.
Hence, it is an is an isoscees triangle.
HOPE IT HELPS YOU....
AD = AD (Common)
angle BAD = angle CAD (given, AD is bisector of angle A)
angle ADB = angle ADC (given, AD is perpendicular to BC)
By SAS,
triangle ABD congruent triangle ACD
By CPCT,
AB = AC
angle ABD = angle ACD
or in an isosceles triangle, opposite sides of a triangle are equal.
Hence, it is an is an isoscees triangle.
HOPE IT HELPS YOU....
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