If the bisector of the vertical angle of a triangle bisects the base ,

1.	If the bisector of the vertical angle of a triangle bisects the base , prove that triangle is an isosceles
Answer» Answer: That's your answer dude 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

If the bisector of the vertical angle of a triangle bisects the base , prove that triangle is an isosceles

Answer»

Answer:

That's your answer dude

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