Question

If the bisector of vertical angle of a triangle is perpendicular to the base of the triangle, then the triangle is:​

Answer 1

Answer:

It is a isoceles triangle

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.

Answer 2

Answer:

Hi I am Guru Tarun I will Tell answer for your Question

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