Draw and describe the locus of vertices of all isosceles triangles having a common base.
Locus
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Question

Draw and describe the locus of vertices of all isosceles triangles having a common base.

KnowledgeBoat · Accepted 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.

Mathematics

Draw and describe the locus of vertices of all isosceles triangles having a common base.

Locus

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