Question

which triangle is congruent to △klm?
a △gjh
b △cba
c △fde
d none

Explanation:

Step1: Recall congruent - triangle criteria

Congruent triangles have equal side - lengths and equal angles. We can check side - lengths using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ or by counting grid units for right - angled triangles formed by the grid.

Step2: Analyze $\triangle KLM$

Count the lengths of the sides of $\triangle KLM$. Let's assume each grid square has a side - length of 1 unit. $KL$ has a length of 2 units (vertical), $LM$ has a length of 3 units (horizontal), and $KM$ can be found using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 2$ and $b = 3$, so $KM=\sqrt{2^{2}+3^{2}}=\sqrt{4 + 9}=\sqrt{13}$.

Step3: Analyze $\triangle GJH$

$GJ$ has a length of 3 units (horizontal), $JH$ has a length of 2 units (vertical), and $GH=\sqrt{2^{2}+3^{2}}=\sqrt{13}$. The side - lengths of $\triangle GJH$ match the side - lengths of $\triangle KLM$.

Step4: Check other triangles

For $\triangle CBA$ and $\triangle FDE$, their side - lengths do not match the side - lengths of $\triangle KLM$.

Answer:

A. $\triangle GJH$