Question

which pairs of figures are congruent? which pairs are similar? congruent? yes no similar? yes no congruent? yes no similar? yes no congruent? yes no similar? yes no congruent? yes no similar? yes no

Explanation:

First pair (two circles):

• Congruent?
• Congruent figures have the same shape and size. The two circles have different sizes (radii), so they are not congruent.
• Similar?
• Similar figures have the same shape. All circles are similar because they have the same general shape (defined by the equation \((x - a)^2+(y - b)^2=r^2\), and the ratio of their radii is a constant for any two circles). So, they are similar.

Second pair (two L - shaped figures):

• Congruent?
• The two L - shaped figures have different sizes. One is larger than the other. So, they are not congruent.
• Similar?
• We can assume that the angles of the L - shapes are right angles (90 degrees). If the ratio of the corresponding side lengths is constant (for example, if we consider the horizontal and vertical segments of the L - shape, and the ratio of the longer segment to the shorter segment is the same for both figures), then they are similar.

Third pair (two triangles):

• Congruent?
• The two triangles have different side lengths (one is “flatter” and the other is more “pointed” in terms of side - length proportions). So, they are not congruent.
• Similar?
• If the angles of the two triangles are not equal (we can assume from the visual appearance that the angle measures are different, for example, the angles of the “flatter” triangle and the more “pointed” triangle), then they are not similar (by the AA (angle - angle) similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar).

Fourth pair (a rectangle and a square):

• Congruent?
• A square has all sides equal, and a rectangle has opposite sides equal. They have different side - length relationships (except in the special case when the rectangle is a square, but here they are distinct). So, they are not congruent.
• Similar?
• A square has four right angles and all sides equal. A rectangle has four right angles but opposite sides equal. The ratio of adjacent sides is not the same (for a square \(a/b = 1\) where \(a\) and \(b\) are side lengths, and for a non - square rectangle \(a/b

eq1\)). So, they are not similar.

Answer:

• First pair: Congruent? No, Similar? Yes.
• Second pair: Congruent? No, Similar? Yes.
• Third pair: Congruent? No, Similar? No.
• Fourth pair: Congruent? No, Similar? No.