Geometry worksheet for students to identify congruent and similar shapes in a house illustration.

To solve the problems related to the image of "The Similar-Congruent House," let's analyze each question step by step.

---

Image Analysis

The house in the image contains various shapes, including windows, doors, and other geometric figures. The task involves identifying congruent and similar shapes based on their properties.

#### Key Definitions:
1. Congruent Shapes: Two shapes are congruent if they have the same size and shape. This means all corresponding sides and angles are equal.
2. Similar Shapes: Two shapes are similar if they have the same shape but not necessarily the same size. This means all corresponding angles are equal, and corresponding sides are proportional.

---

Solutions to Each Question

#### 1. Which window is congruent to window B?
- Window B is a square with four equal sides.
- Looking at the other windows:
- Window C is also a square with four equal sides.
- Windows D, E, and F are rectangles, not squares.
- Therefore, window C is congruent to window B.

Answer: C

---

#### 2. Is the window on the door congruent to the windows on the roof?
- The window on the door is a rectangle.
- The windows on the roof are squares.
- A rectangle and a square are not congruent because their side lengths are different (even if they might be similar in shape).
- Therefore, the window on the door is not congruent to the windows on the roof.

Answer: No

---

#### 3. Name one rectangle that is similar to D?
- Rectangle D is a rectangle with specific dimensions.
- To find a rectangle similar to D, we need another rectangle with the same proportions but possibly different sizes.
- Rectangle E has the same proportions as D but is smaller.
- Therefore, rectangle E is similar to rectangle D.

Answer: E

---

#### 4. Name a shape that is congruent to M?
- Shape M is a circle.
- Looking at the other shapes:
- Shape N is also a circle with the same radius.
- Therefore, shape N is congruent to shape M.

Answer: N

---

#### 5. How many shapes are congruent to N?
- Shape N is a circle.
- The only other circle in the image is M, which is congruent to N.
- Therefore, there is 1 shape congruent to N.

Answer: 1

---

#### 6. Is Q congruent to R?
- Shape Q is a triangle.
- Shape R is also a triangle.
- Both triangles appear to have the same side lengths and angles, making them congruent.
- Therefore, Q is congruent to R.

Answer: Yes

---

#### 7. How many shapes are congruent to S?
- Shape S is a triangle.
- Looking at the other shapes:
- Shape T is also a triangle with the same side lengths and angles.
- Therefore, there is 1 shape congruent to S.

Answer: 1

---

#### 8. Draw two more windows on the house. Make the windows similar, but not congruent.
- To draw two windows that are similar but not congruent:
- Choose a shape for the window (e.g., a square or a rectangle).
- Ensure the new windows have the same proportions as an existing window but different sizes.
- For example:
- If you choose a square, draw two larger squares with the same proportions as window B or C.
- If you choose a rectangle, draw two rectangles with the same proportions as window D or E but different sizes.

Explanation: Similar shapes have the same shape but different sizes. Congruent shapes have the same size and shape. By ensuring the new windows have the same proportions as existing windows but different sizes, they will be similar but not congruent.

---

Final Answers

1. C
2. No
3. E
4. N
5. 1
6. Yes
7. 1
8. Draw two windows with the same proportions as an existing window but different sizes.

---

Boxed Final Answer

\[
\boxed{
\begin{array}{l}
1. \text{C} \\
2. \text{No} \\
3. \text{E} \\
4. \text{N} \\
5. \text{1} \\
6. \text{Yes} \\
7. \text{1} \\
8. \text{Draw two windows with the same proportions as an existing window but different sizes.}
\end{array}
}
\]