1.
a)
ΔADC
[tex]|AD|^{2} +|CD|^{2} =|AC|^{2}[/tex]
ΔBCD
[tex]|BD|^{2} +|CD|^{2} =|BC|^{2}[/tex]
b)
ΔEHI
[tex]|EI|^{2} +|HI|^{2} =|EH|^{2}[/tex]
ΔFGJ
[tex]|FJ|^{2} +|GJ|^{2} =|FG|^{2}[/tex]
c)
ΔKLM
[tex]|KL|^{2} +|LM|^{2} =|KM|^{2}[/tex]
ΔKLN
[tex]|KL|^{2} +|KN|^{2} =|LN|^{2}[/tex]
ΔKMN
[tex]|MN|^{2} +|KN|^{2} =|KM|^{2}[/tex]
ΔLMN
[tex]|MN|^{2} +|LM|^{2} =|LN|^{2}[/tex]
2.
[tex]5^{2} + h^{2} =11^{2}\\ h^{2} =121-25=96\\h=\sqrt{96} =4\sqrt{6} \\P=\frac{1}{2} *10*4\sqrt{6}=20\sqrt{6}[/tex]
3.
[tex](-2)^{2} +(-4)^{2} = x^{2} \\4+16=x^{2} \\x^{2} =20\\x=2\sqrt{5}[/tex]
4.
A(2, 4) B(2, -1) C(-3, -1)
|AB|=5 |BC|=5 ∡B=90°
[tex]P=\frac{1}{2}*5*5=12,5[/tex]
