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 (Rectangles):

• Congruent?
• Congruent figures have the same shape and size. The two rectangles have different side - length proportions (one is more "squashed" horizontally). So, they are not congruent.
• Similar?
• Similar figures have the same shape (corresponding angles are equal, and side - length ratios are equal). For rectangles, all angles are \(90^{\circ}\). But if the ratio of length to width for one rectangle is \(l_1/w_1\) and for the other is \(l_2/w_2\), and \(l_1/w_1

eq l_2/w_2\) (by visual inspection of side - length proportions), they are not similar.

Second Pair (Triangles):

• Congruent?
• Congruent triangles must have all corresponding sides and angles equal. By visual inspection (different side lengths), they are not congruent.
• Similar?
• Both are right - angled triangles (assuming the right angles are present as per the shape). For two right - angled triangles, if the ratios of their corresponding sides are equal, they are similar. Let the sides of the smaller triangle be \(a,b,c\) (right - angled) and of the larger triangle be \(A,B,C\). If \(\frac{a}{A}=\frac{b}{B}=\frac{c}{C}\) (by the property of similar right - angled triangles, and since the angles of a right - angled triangle are \(90^{\circ},\theta,90 - \theta\) and the angles will be equal for both triangles as they have the same general shape), they are similar.

Third Pair (T - shaped figures):

• Congruent?
• Congruent figures have the same shape and size. By visual inspection (different orientations and side - length relationships in terms of overall size), they are not congruent.
• Similar?
• Similar figures have the same shape. If we consider the "T - shape" as composed of rectangles, the ratios of corresponding lengths (vertical and horizontal parts) are not equal (by visual inspection of side - length proportions), so they are not similar.

Fourth Pair (Circles):

• Congruent?
• Congruent circles have the same radius. By visual inspection (different sizes), they are not congruent.
• Similar?
• All circles are similar. The ratio of their radii \(r_1/r_2\) (a constant for any two circles) satisfies the similarity condition (for circles, the shape is determined only by the circular form, and the ratio of corresponding linear measures - radii - is a constant).

Answer:

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