Regular Shapes - Free Printable

Problem Description:

The task is to identify the regular shapes from a given set of geometric figures. A regular shape is defined as a polygon where all sides are of equal length and all interior angles are equal.

Solution Approach:

1. Understand the Definition of Regular Shapes:
- A regular shape must have:
- All sides of equal length.
- All interior angles of equal measure.
- Examples include equilateral triangles, squares, regular pentagons, regular hexagons, etc.

2. Analyze Each Shape in the Image:
- Carefully examine each figure to determine if it meets the criteria for being a regular shape.
- Exclude any shapes that are irregular (e.g., rectangles, parallelograms, or stars).

3. Identify and Highlight Regular Shapes:
- Mark the shapes that are regular by checking their side lengths and angles.

Step-by-Step Analysis:

#### Row 1:
- Shape 1: Equilateral triangle (all sides equal, all angles equal) → Regular
- Shape 2: Trapezoid (not all sides equal) → Not Regular
- Shape 3: Equilateral triangle (all sides equal, all angles equal) → Regular
- Shape 4: Rectangle (opposite sides equal, but not all sides equal) → Not Regular

#### Row 2:
- Shape 1: Regular pentagon (all sides equal, all angles equal) → Regular
- Shape 2: Parallelogram (opposite sides equal, but not all sides equal) → Not Regular
- Shape 3: Semi-circle (not a polygon) → Not Regular
- Shape 4: Isosceles triangle (two sides equal, but not all sides equal) → Not Regular

#### Row 3:
- Shape 1: Rhombus (all sides equal, but angles not equal) → Not Regular
- Shape 2: Circle (not a polygon) → Not Regular
- Shape 3: Regular octagon (all sides equal, all angles equal) → Regular
- Shape 4: Arrow (not a polygon) → Not Regular

#### Row 4:
- Shape 1: Cross (not a polygon with equal sides and angles) → Not Regular
- Shape 2: Square (all sides equal, all angles equal) → Regular
- Shape 3: Right triangle (not all sides equal) → Not Regular
- Shape 4: Rhombus (all sides equal, but angles not equal) → Not Regular

#### Row 5:
- Shape 1: Regular octagon (all sides equal, all angles equal) → Regular
- Shape 2: Trapezoid (not all sides equal) → Not Regular
- Shape 3: Star (not all sides equal, not all angles equal) → Not Regular
- Shape 4: Parallelogram (opposite sides equal, but not all sides equal) → Not Regular

Final Answer:

The regular shapes are highlighted in red in the image. Based on the analysis, the regular shapes are:
- Equilateral triangles (Row 1, Shapes 1 and 3)
- Regular pentagon (Row 2, Shape 1)
- Regular octagon (Row 3, Shape 3)
- Square (Row 4, Shape 2)
- Regular octagon (Row 5, Shape 1)

Thus, the final answer is:
\[
\boxed{\text{Equilateral triangles, Regular pentagon, Regular octagon, Square, Regular octagon}}
\]