Question

which pairs of figures are congruent? which pairs are similar?
(first figure: a small circle and a large ellipse; below: congruent? ∘ yes ∘ no; similar? ∘ yes ∘ no)
(second figure: a large t shape and a small t shape; below: congruent? ∘ yes ∘ no; similar? ∘ yes ∘ no)
(third figure: a small rectangle and a tall rectangle; below: congruent? ∘ yes ∘ no; similar? ∘ yes ∘ no)
(fourth figure: a small triangle and a small triangle; below: congruent? ∘ yes ∘ no; similar? ∘ yes ∘ no)

Explanation:

First Pair (Circle and Oval)

• Congruent?
• Congruent figures have same shape and size. A circle and an oval (ellipse) have different shapes.
• Similar?
• Similar figures have same shape. A circle and an oval (ellipse) have different shapes.

Second Pair (Two “T” - shaped figures)

• Congruent?
• Congruent figures have same shape and size. The two “T” - shaped figures have different sizes.
• Similar?
• Similar figures have same shape. The two “T” - shaped figures have the same shape (one is a scaled - down version of the other).

Third Pair (Two Rectangles)

• Congruent?
• Congruent figures have same shape and size. The two rectangles have different side - length ratios (one is a square - like rectangle and the other is more elongated).
• Similar?
• Similar figures have same shape. The two rectangles have different side - length ratios (for similar rectangles, \(\frac{l_1}{w_1}=\frac{l_2}{w_2}\), which is not the case here).

Fourth Pair (Two Triangles)

• Congruent?
• Congruent figures have same shape and size. The two triangles have different sizes.
• Similar?
• Similar figures have same shape. The two triangles have the same shape (they are both right - angled triangles, and if we assume the angles are equal, by AA (angle - angle) similarity criterion for triangles).

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