the bisector of a vertical angle of a triangle is perpendicular to the base of a triangle is
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Answer:
✰ HI MATE ! ✰
QUESTION :- ⬇️ ➦
If the bisector of the vertical angle of a triangle bisects the base, show that the triangle is isosceles.
ANSWER :- ⬇️ ➨
Given △ABC, AD is a bisector of ∠A which meets base BC at D such that BD = DC.
Produce AD to meet E such that AD = ED.
Now, in △ABD and △DEC
BD=DC ...... [Given]
AD=DE ........ [By construction]
∠ADB=∠EDC ..... [Vertically opposite angles]
∴ △ABD ≅△EDC [∵SAS congruence ]
⟹ AB=EC and ∠BAD=∠DEC ..... [CPCT]
Also, ∠BAD=∠DAC
⟹ ∠DAC=∠DEC
⟹ In △ACE, ∠AEC=∠CAE
⟹ AC=CE ........ [Sides opposite to equal angles]
⟹ AB=AC
Hence, △ABC is isosceles.
✅ HENCE, VERIFIED ✅
Hope my answer helps you Dear.. ✌️❤️
Pls mark as brainliest.. ♕.
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Answer:
Hi I will tell answer
Step-by-step explanation:
Given △ABC, AD is a bisector of ∠A which meets base BC at D such that BD = DC.
Produce AD to meet E such that AD = ED.
Now, in △ABD and △DEC
BD=DC ...... [Given]
AD=DE ........ [By construction]
∠ADB=∠EDC ..... [Vertically opposite angles]
∴ △ABD ≅△EDC [∵SAS congruence ]
⟹ AB=EC and ∠BAD=∠DEC ..... [CPCT]
Also, ∠BAD=∠DAC
⟹ ∠DAC=∠DEC
⟹ In △ACE, ∠AEC=∠CAE
⟹ AC=CE ........ [Sides opposite to equal angles]
⟹ AB=AC
Hence, △ABC is isosceles.
HENCE, VERIFIED