identifying congruent figures on a grid
Check the final answer first, then review the worked steps.
Problem
identifying congruent figures on a grid
Answer
Top-left: Yes, Top-right: No, Bottom-left: Yes, Bottom-right: No
Step-by-step solution
- Definition of Congruence: Two figures are congruent if they have the exact same shape and size. This means one figure can be mapped onto the other through rigid transformations (translation, rotation, or reflection).
- Analyze the first pair (top left): The two trapezoids have the same dimensions. Counting the grid units, both have a top base of 2 units, a bottom base of 4 units, and a height of 3 units. Since they are identical in size and shape, they are congruent. Answer: Yes.
- Analyze the second pair (top right): The two circles have different radii. The top circle has a diameter of 2 units, while the bottom circle has a diameter of 4 units. Because their sizes are different, they are not congruent. Answer: No.
- Analyze the third pair (bottom left): Both rectangles have a width of 2 units and a height of 4 units. Since they have the same dimensions, they are congruent. Answer: Yes.
- Analyze the fourth pair (bottom right): The first triangle is a right-angled triangle with base 3 and height 2. The second triangle is an isosceles triangle with base 4 and height 4. Since the shapes and sizes are different, they are not congruent. Answer: No.