Question

which pairs of figures are congruent? which pairs are similar?

Explanation:

First Pair (Circles)

• Congruent: Congruent figures have the same shape and size. The two circles have different sizes (one is larger than the other). So, for congruent: No.
• Similar: Similar figures have the same shape. Both are circles (same shape). So, for similar: Yes.

Second Pair (T - shaped figures)

• Congruent: Congruent figures have the same shape and size. The two T - shaped figures have different sizes (one is larger than the other). So, for congruent: No.
• Similar: Similar figures have the same shape. Both have the T - like shape (same shape). So, for similar: Yes.

Third Pair (Rectangles)

• Congruent: Congruent figures have the same shape and size. The two rectangles have different sizes (one is taller - thinner, the other is shorter - wider). So, for congruent: No.
• Similar: Similar figures have the same shape. For rectangles, similarity requires that the ratios of corresponding sides are equal. Let's assume the side lengths. If the top rectangle has length \(l_1\) and width \(w_1\), and the bottom rectangle has length \(l_2\) and width \(w_2\), if \(\frac{l_1}{l_2}

eq\frac{w_1}{w_2}\), they are not similar. In a grid - based (assuming uniform grid) case, if one rectangle is \(2\times3\) and the other is \(3\times4\) (ratios \(\frac{2}{3}
eq\frac{3}{4}\)), they are not similar. So, for similar: No.

Fourth Pair (Triangles)

• Congruent: Congruent figures have the same shape and size. The two triangles have different sizes (one is larger than the other). So, for congruent: No.
• Similar: Similar figures have the same shape. For triangles, similarity can be checked by AA (angle - angle), SSS (side - side - side) or SAS (side - angle - side) criteria. Assuming in a grid (with right - angled triangles for simplicity), if the ratios of corresponding sides are equal. If one triangle has sides \(a,b,c\) and the other has sides \(ka,kb,kc\) (\(k

eq1\)), they are similar. In a typical grid - based non - congruent but same - shape (e.g., \(1 - 2-\sqrt{5}\) and \(2 - 4 - 2\sqrt{5}\) right - angled triangles), they are similar. So, for similar: Yes.

Answer:

• First Pair: Congruent? No; Similar? Yes.
• Second Pair: Congruent? No; Similar? Yes.
• Third Pair: Congruent? No; Similar? No.
• Fourth Pair: Congruent? No; Similar? Yes.