Answer:
Step-by-step explanation:
1)
[tex]AB^2 = BD^2 + AD^2\\[/tex] ------- ( 1 )
[tex]= 4^2 + (2\sqrt6)^2\\\\=16 + (4 \times 6)\\\\= 16 + 24\\\\= 40[/tex]
[tex]AB = \sqrt {40} = \sqrt {4 \times 10} = 2\sqrt{10}[/tex]
2)
[tex]AC^2 = AD^2 + DC^2[/tex] --------------( 2 )
[tex]=(2 \sqrt6)^2 + 6^2 \\\\= 24 + 36\\\\=60[/tex]
[tex]AC= \sqrt{60} = \sqrt{4 \times 15} = 2 \sqrt{15}[/tex]
3)
BC² = AB² + AC²
(4 + 6)² = 40 + 60
100 = 100
Satisfies Pythagoras Theorem, therefore triangle ABC is right angles triangle.
