Math Problem Statement

Which pairs of figures below are congruent?

Solution

The problem involves identifying pairs of congruent shapes. Congruent shapes are identical in size and shape, though they may be rotated or reflected. Let's analyze each pair of shapes from the image:

  1. Top Left Pair (Triangles):

    • The two shapes are triangles. Despite the orientation, they appear to be identical in size and shape.
    • Answer: Yes, they are congruent.
  2. Top Right Pair (L-shaped figures):

    • These shapes are L-shaped, and they appear to be the same size but are rotated. Since rotations do not affect congruence, they are congruent.
    • Answer: Yes, they are congruent.
  3. Bottom Left Pair (Square and Rectangle):

    • One shape is a square, and the other is a rectangle. Since their side lengths are different, they are not congruent.
    • Answer: No, they are not congruent.
  4. Bottom Right Pair (Circle and Oval):

    • One shape is a circle, and the other is an oval (ellipse). Since these have different shapes, they are not congruent.
    • Answer: No, they are not congruent.

Let me know if you'd like more details or have questions.

Here are 5 related questions to explore:

  1. What transformations preserve congruence (e.g., rotation, reflection)?
  2. How does congruence differ from similarity?
  3. Can two polygons with different numbers of sides be congruent?
  4. What is the relationship between symmetry and congruence?
  5. How do we prove that two complex shapes are congruent?

Tip: Congruence only depends on the size and shape of the figures, not their orientation or position.

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Math Problem Analysis

Mathematical Concepts

Congruence
Geometry
Transformations

Formulas

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Theorems

Congruence Theorem

Suitable Grade Level

Grades 6-8