Worksheet to identify congruent and non-congruent shapes.

Problem Analysis:

The task involves identifying which pairs of figures are congruent and which are not congruent. Two figures are congruent if they have the same shape and size, meaning one figure can be transformed into the other through translation, rotation, or reflection without any change in size.

Let's solve each question step by step.

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Question 1: Which of the following pair of figures are congruent?

#### Options:
- a) Two squares
- b) A square and a rectangle
- c) Two rectangles

#### Solution:
- Option a: Both figures are squares. Squares are always congruent if their side lengths are equal. Since no specific dimensions are given, we assume they are the same size.
- Option b: One figure is a square, and the other is a rectangle. Squares and rectangles are not congruent because they have different shapes (all sides of a square are equal, while a rectangle has two pairs of equal sides).
- Option c: Both figures are rectangles. However, the rectangles appear to have different dimensions (one looks longer and narrower than the other), so they are not congruent.

#### Correct Answer: a)

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Question 2: Which of the following pair of figures are congruent?

#### Options:
- a) Two triangles with different orientations
- b) Two identical triangles
- c) A triangle and a smaller triangle

#### Solution:
- Option a: The two triangles have the same shape and size but are oriented differently. Congruent figures can be rotated or reflected, so these triangles are congruent.
- Option b: The two triangles are identical in shape and size. They are clearly congruent.
- Option c: One triangle is smaller than the other. Figures that differ in size are not congruent.

#### Correct Answer: b)

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Question 3: Which of the following pair of figures are not congruent?

#### Options:
- a) Two circles
- b) A circle and an oval
- c) An oval and another oval

#### Solution:
- Option a: Both figures are circles. Circles are congruent if they have the same radius. Assuming the circles are the same size, they are congruent.
- Option b: One figure is a circle, and the other is an oval. Circles and ovals have different shapes, so they are not congruent.
- Option c: Both figures are ovals. However, the ovals appear to have different proportions (one is more elongated than the other), so they are not congruent.

#### Correct Answer: b)

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Question 4: Which of the following pair of figures are congruent?

#### Options:
- a) Two arrows pointing in opposite directions
- b) A cross and a plus sign
- c) A rhombus and a square

#### Solution:
- Option a: Both figures are arrows with the same shape and size but pointing in opposite directions. Congruent figures can be reflected, so these arrows are congruent.
- Option b: The cross and the plus sign have the same shape and size. They are congruent.
- Option c: One figure is a rhombus, and the other is a square. While both have four equal sides, a square has right angles, whereas a rhombus does not necessarily have right angles. Therefore, they are not congruent.

#### Correct Answer: a)

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Question 5: Which of the following pair of figures are not congruent?

#### Options:
- a) Two half-circles
- b) Two diamonds
- c) Two triangles

#### Solution:
- Option a: Both figures are half-circles. Half-circles are congruent if they have the same radius. Assuming the half-circles are the same size, they are congruent.
- Option b: Both figures are diamonds (rhombuses). Diamonds are congruent if they have the same side lengths and angles. Assuming the diamonds are the same size and shape, they are congruent.
- Option c: Both figures are triangles. However, the triangles appear to have different shapes (one is wider and shorter, while the other is taller and narrower), so they are not congruent.

#### Correct Answer: c)

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Final Answers:

1. a)
2. b)
3. b)
4. a)
5. c)

Boxed Final Answer:
\[
\boxed{a, b, b, a, c}
\]