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 (Triangles)

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

Second Pair (L - shaped figures)

• Congruent?
• Congruent figures have the same shape and size. The two L - shaped figures have different orientations and sizes (when considering side lengths in terms of grid units, they don't match exactly in all dimensions). So, the answer for congruent is \(No\).
• Similar?
• Similar figures have the same shape. The first L - shaped figure is “taller” and the second is “wider” (in terms of the grid), so their side - length ratios are not equal. So, the answer for similar is \(No\).

Third Pair (Squares)

• Congruent?
• Congruent figures have the same shape and size. Both are squares. Assuming they have the same side - length (as per the grid representation, if we consider unit - based side lengths). So, the answer for congruent is \(Yes\).
• Similar?
• Since congruent figures are a special case of similar figures (with a scale factor of \(1\)). So, the answer for similar is \(Yes\).

Fourth Pair (Oval and Circle)

• Congruent?
• Congruent figures have the same shape and size. An oval and a circle have different shapes. So, the answer for congruent is \(No\).
• Similar?
• Similar figures have the same shape. An oval and a circle have different geometric properties (a circle has \(r_1 = r_2\), an oval has \(r_1

eq r_2\) in its standard form \(\frac{(x - h)^2}{r_1^2}+\frac{(y - k)^2}{r_2^2}=1\)). So, the answer for similar is \(No\).

Answer:

• First Pair: Congruent? \(No\), Similar? \(Yes\)
• Second Pair: Congruent? \(No\), Similar? \(No\)
• Third Pair: Congruent? \(Yes\), Similar? \(Yes\)
• Fourth Pair: Congruent? \(No\), Similar? \(No\)