Question

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are △bcd and △ghi congruent?

Explanation:

Step1: Calculate the side lengths of \(\triangle BCD\)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(BC\): \(B(0,0)\), \(C(- 10,0)\), \(d_{BC}=\sqrt{(0 + 10)^2+(0 - 0)^2}=10\).
For \(BD\): \(B(0,0)\), \(D(-5,6)\), \(d_{BD}=\sqrt{(0 + 5)^2+(0 - 6)^2}=\sqrt{25 + 36}=\sqrt{61}\).
For \(CD\): \(C(-10,0)\), \(D(-5,6)\), \(d_{CD}=\sqrt{(-5 + 10)^2+(6 - 0)^2}=\sqrt{25+36}=\sqrt{61}\).

Step2: Calculate the side lengths of \(\triangle GHI\)

For \(GH\): \(G(0,10)\), \(H(9,10)\), \(d_{GH}=\sqrt{(9 - 0)^2+(10 - 10)^2}=9\).
Since \(BC = 10
eq GH=9\), the two triangles are not congruent.

Answer:

\(\triangle BCD\) and \(\triangle GHI\) are not congruent.