Question

segments and angles
identifying congruent shapes on a grid
which pairs of figures below are congruent?
(images of figure pairs and congruent? options with yes/no radio buttons)

Explanation:

Congruent shapes have identical size and shape, meaning one can be mapped to the other via rigid transformations (translation, rotation, reflection) without resizing.

1. Top-left pair (circles): Both circles have the same diameter (spanning 4 grid units), so they are congruent.
2. Top-right pair (triangles): The triangles have different side lengths (smaller triangle has 3-unit sides, larger has 6-unit sides), so they are not congruent.
3. Bottom-left pair (rectangles): The rectangles have different dimensions (one is 3x2, the other is 2x3, which are rotations but same side lengths, so congruent).
4. Bottom-right pair (trapezoids): Both trapezoids have identical base lengths and height (top base 2 units, bottom base 4 units, height 3 units), so they are congruent.

Answer:

Top-left pair: Yes
Top-right pair: No
Bottom-left pair: Yes
Bottom-right pair: Yes