Geometry Riddles 3A worksheet featuring riddles and shapes for students to solve.

Let's solve each riddle step by step using the clues and the shapes provided.

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Riddle 1:

> - I have no right angles.
> - I am not a quadrilateral.
> - All my sides are equal length.
> - I have more than 4 sides.
> - Who am I?

Let’s go through the clues:

1. No right angles → So we eliminate any shape with 90° angles.
2. Not a quadrilateral → So it cannot have 4 sides. Eliminate shapes with 4 sides (like squares, rectangles, rhombuses, trapezoids, etc.).
3. All sides are equal length → So it must be equilateral.
4. More than 4 sides → So it has at least 5 sides.

Now look at the options:

- A – Triangle → 3 sides → Not more than 4 → ✘
- B – Parallelogram → 4 sides → Quadrilateral → ✘
- C – Trapezoid → 4 sides → Quadrilateral → ✘
- D – L-shaped → Not all sides equal, has right angles → ✘
- E – Rectangle → 4 sides → Quadrilateral → ✘
- F – Right triangle → Has right angle → ✘
- G – Circle → No sides → But “all sides equal” doesn’t apply → ✘
- H – Rhombus → 4 sides → Quadrilateral → ✘
- I – Hexagon → 6 sides → More than 4 → Not a quadrilateral → All sides equal? Yes, in a regular hexagon → No right angles? Yes → ✔

✔ So Shape I (Regular Hexagon) fits:
- No right angles → ✔️
- Not a quadrilateral → ✔️
- All sides equal → ✔️
- More than 4 sides → ✔️

👉 Answer to Riddle 1: Shape I

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Riddle 2:

> - I am a quadrilateral.
> - I have one line of symmetry.
> - I have one pair of parallel lines.
> - Who am I?

Let’s analyze:

1. Quadrilateral → 4 sides → So we only consider A, B, C, D, E, F, H (but F is a triangle → ✘)
- Wait: F is a triangle → 3 sides → ✘
- So possible: A, B, C, D, E, H

But let’s check which ones are quadrilaterals:
- A: Triangle → ✘
- B: Parallelogram → 4 sides → ✔️
- C: Trapezoid → 4 sides → ✔️
- D: L-shape → 4 sides → But not a standard quadrilateral? Actually, it has 4 sides but is irregular → Still a quadrilateral? Technically yes, but let’s see if it matches the rest.
- E: Rectangle → 4 sides → ✔️
- H: Rhombus → 4 sides → ✔️

Now:
- One line of symmetry → So it can't have more than one.
- One pair of parallel lines → So only one pair of opposite sides are parallel.

Let’s evaluate:

- B (Parallelogram): Two pairs of parallel sides → ✘ (needs only one pair)
- C (Trapezoid): One pair of parallel sides → ✔️
- Does it have one line of symmetry? Only if it’s an isosceles trapezoid, which this appears to be (top and bottom parallel, non-parallel sides equal). Yes → It has one vertical line of symmetry → ✔️
- D (L-shape): Not symmetric → No line of symmetry → ✘
- E (Rectangle): Two lines of symmetry (horizontal and vertical) → ✘ (only one allowed)
- H (Rhombus): Two lines of symmetry (diagonals) → ✘
- A & F: Not quadrilaterals → ✘

So only C (Trapezoid) satisfies:
- Quadrilateral → ✔️
- One pair of parallel lines → ✔️
- One line of symmetry → ✔️

👉 Answer to Riddle 2: Shape C

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✔ Final Answers:

1) Shape I
2) Shape C

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🟩 Summary:

- Riddle 1: Regular Hexagon → Shape I
- Riddle 2: Isosceles Trapezoid → Shape C

You’ve solved the geometry riddles! 😊