Question

which pairs of figures are congruent? which pairs are similar?

(first grid with two triangles)
congruent? ○ yes ○ no
similar? ○ yes ○ no

(second grid with two t - like figures)
congruent? ○ yes ○ no
similar? ○ yes ○ no

(third grid with two rectangles)
congruent? ○ yes ○ no
similar? ○ yes ○ no

(fourth grid with a circle and an ellipse)
congruent? ○ yes ○ no
similar? ○ yes ○ no

Explanation:

Top - Left Pair (Triangles)

Step1: Check Congruence

Congruent figures have same shape and size. The two triangles have different shapes (one is a right - angled triangle, the other is a more "stretched" triangle) and different sizes. So congruent? No.

Step2: Check Similarity

Similar figures have the same shape (corresponding angles equal) and proportional sides. The angles of the two triangles are not the same (one has a right angle, the other does not seem to have a right angle in the same way), so their shapes are different. So similar? No.

Top - Right Pair (T - shaped figures)

Step1: Check Congruence

Congruent figures must have the same shape and size. The two T - shaped figures have different orientations and also, if we look at the structure, their shapes (the way the squares are arranged) are such that they are not the same size or shape. So congruent? No.

Step2: Check Similarity

Similar figures have the same shape (corresponding angles equal and sides proportional). The two T - shaped figures have different shapes (one is a "plus - like" T and the other is a "minus - like" T in terms of orientation and structure), so their shapes are not the same. So similar? No.

Bottom - Left Pair (Rectangles)

Step1: Check Congruence

Congruent figures have same shape and size. The two rectangles have different sizes (the top rectangle is taller and narrower, the bottom one is shorter and wider) and same shape (both are rectangles). But since size is different, congruent? No.

Step2: Check Similarity

Similar figures have same shape (all angles are right angles for rectangles, so corresponding angles are equal) and proportional sides. Let the length and width of the top rectangle be \(l_1,w_1\) and bottom be \(l_2,w_2\). The ratios \(\frac{l_1}{l_2}\) and \(\frac{w_1}{w_2}\) are not equal (since one is taller and narrower, the other shorter and wider), so sides are not proportional. So similar? No.

Bottom - Right Pair (Circle and Ellipse)

Answer:

• Top - Left Pair:
• Congruent? No
• Similar? No
• Top - Right Pair:
• Congruent? No
• Similar? No
• Bottom - Left Pair:
• Congruent? No
• Similar? No
• Bottom - Right Pair:
• Congruent? No
• Similar? No