Question

which pairs of figures are congruent? which pairs are similar?
(there are four groups of figures with grids and options for congruent and similar:

1. two triangles, options yes/no for congruent and similar.
2. two cross - shaped figures, options yes/no for congruent and similar.
3. two squares, options yes/no for congruent and similar.
4. a circle and an ellipse, options yes/no for congruent and similar.)

Explanation:

Step1: Analyze Top - Left Figures (Triangles)

Congruent: Congruent figures have the same shape and size. The two triangles have different sizes, so congruent is No. Similar: Similar figures have the same shape (corresponding angles equal, corresponding sides in proportion). The two triangles have the same shape (both are triangles with the same angle structure), so similar is Yes.

Step2: Analyze Top - Right Figures (Cross - like Shapes)

Congruent: The two cross - like shapes have different orientations and we can check their size and shape. They are not the same size, so congruent is No. Similar: They have the same shape (the same number of sides and the same overall structure), so similar is Yes.

Step3: Analyze Bottom - Left Figures (Squares)

Congruent: The two squares have the same shape and size (since they are both squares and look to have the same side length on the grid), so congruent is Yes. Similar: All congruent figures are similar (since if they are congruent, their corresponding sides are in proportion (ratio 1:1) and corresponding angles are equal), so similar is Yes.

Step4: Analyze Bottom - Right Figures (Circle and Oval)

Congruent: A circle and an oval have different shapes (a circle has all points equidistant from the center, an oval is an ellipse), so congruent is No. Similar: Similar figures must have the same shape. Since a circle and an oval have different shapes, similar is No.

Answer:

• Top - Left: Congruent? No; Similar? Yes
• Top - Right: Congruent? No; Similar? Yes
• Bottom - Left: Congruent? Yes; Similar? Yes
• Bottom - Right: Congruent? No; Similar? No