Question

are the following two figures similar or congruent?

Explanation:

Step1: Calculate the side lengths of the rectangles

For the green rectangle \(DEFG\):

• Length (horizontal side): Count the units along the \(x -\)axis. From \(x = 1\) to \(x = 5\), so length \(l_1=5 - 1=4\) units.
• Width (vertical side): Count the units along the \(y -\)axis. From \(y = 2\) to \(y = 3\), so width \(w_1=3 - 2 = 1\) unit.

For the pink rectangle \(HIJK\):

• Length (vertical side): Count the units along the \(y -\)axis. From \(y=-1\) to \(y = - 5\), so length \(l_2=-1-(-5)=4\) units.
• Width (horizontal side): Count the units along the \(x -\)axis. From \(x=-3\) to \(x=-2\), so width \(w_2=-2-(-3) = 1\) unit.

Step2: Check the congruence condition

Two rectangles are congruent if their corresponding side lengths are equal.
We have \(l_1 = l_2=4\) and \(w_1=w_2 = 1\). Also, all angles in rectangles are right - angles (\(90^{\circ}\)).

Answer:

congruent