Mathematics
Draw and describe the locus of vertices of all isosceles triangles having a common base.
Locus
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Answer
△ABC is an isosceles triangle in which AB = AC.
From A, draw AD perpendicular to BC.
In △ABD and △ACD
AD = AD (Common sides)
AB = AC (Since, triangle is isosceles)
∠ADB = ∠ADC (90°)
Hence, by SAS axiom △ABD ~ △ACD. Since, triangles are similar so the ratio of the corresponding sides will be equal,
Since, BD = DC so AD can be said as the perpendicular bisector of BC.
Hence, the locus of vertices will be the perpendicular bisector of the base.
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