if triangle abc is isosceles and ad is the altitude from a on bc prove that ad bisects bc
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Given : ABC is isosceles ∆ where AD is attitude.
To prove : BD = CD.
Proof : In ∆s ABD and ACD we have,
AB = AC [ Given ]
AD = AD [ Common ]
< ADB = < ADC [ 90° each ]
Hence both triangles are congruent by RHS congruency.
Therefore, BD = CD [ c.p.c.t ]
So, AD bisects BC.
ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ ǫ.ᴇ.ᴅ
Have great future ahead!
Given : ABC is isosceles ∆ where AD is attitude.
To prove : BD = CD.
Proof : In ∆s ABD and ACD we have,
AB = AC [ Given ]
AD = AD [ Common ]
< ADB = < ADC [ 90° each ]
Hence both triangles are congruent by RHS congruency.
Therefore, BD = CD [ c.p.c.t ]
So, AD bisects BC.
ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ ǫ.ᴇ.ᴅ
Have great future ahead!
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