https://file.aiquickdraw.com/mathbot/file/17310184105138vc5mxaa.jpg

Let's go through each question on the worksheet in detail and solve them step-by-step:

### 1. True or False Questions
   - **A. An Equilateral triangle could also be a Scalene triangle.**  
     **Answer:** False. An equilateral triangle has all sides equal, while a scalene triangle has all sides unequal, so they cannot be the same.
   
   - **B. An Isosceles triangle could also be a Scalene triangle.**  
     **Answer:** False. An isosceles triangle has at least two equal sides, while a scalene triangle has all sides unequal, so they cannot be the same.
   
   - **C. An Isosceles triangle could also be a Right triangle.**  
     **Answer:** True. An isosceles triangle can have a right angle if the other two angles are each 45 degrees.
   
   - **D. An Obtuse triangle could also be a Right triangle.**  
     **Answer:** False. An obtuse triangle has one angle greater than 90 degrees, while a right triangle has exactly one 90-degree angle. They cannot be the same.
   
   - **E. A polygon must be either concave or convex.**  
     **Answer:** True. Every polygon is either concave (having at least one interior angle greater than 180°) or convex (all interior angles less than 180°).

### 2. Triangle Side Lengths: 12, 26, and X
   - To find the possible values of \( X \), use the triangle inequality theorem:
     - \( X + 12 > 26 \)
     - \( X + 26 > 12 \)
     - \( 12 + 26 > X \)
     
     Simplifying each:
     - \( X > 14 \)
     - \( X > -14 \) (always true, so it doesn't affect the range)
     - \( X < 38 \)
     
     **Possible values for \( X \):** \( 14 < X < 38 \).

### 3. Draw Each Shape
   - For this question, you would draw:
     - An **Isosceles Trapezoid** with two parallel sides and two equal-length non-parallel sides.
     - A **Rhombus** with all sides equal and opposite angles equal.
     - A **Square** with all sides equal and all angles 90 degrees.

   Ensure to mark congruent angles and sides, and label parallel sides as requested.

### 4. Regular Hexagon with Side Length 24 cm
   - To find the radius of a regular hexagon (distance from the center to a vertex), note that in a regular hexagon, the radius is equal to the side length.
     - **Radius = 24 cm.**

### 5. Formula for the Sum of Interior Angles of a Polygon
   - The formula to find the sum of the interior angles of a polygon with \( n \) sides is:
     \[
     \text{Sum of interior angles} = (n - 2) \times 180^\circ
     \]
   
   - **For a 36-sided polygon:**
     \[
     \text{Sum} = (36 - 2) \times 180^\circ = 34 \times 180^\circ = 6120^\circ
     \]

### 6. Formula for One Interior Angle of a Regular Polygon
   - The formula to find one interior angle of a regular polygon with \( n \) sides is:
     \[
     \text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n}
     \]
   
   - **For a 24-sided polygon:**
     \[
     \text{Interior angle} = \frac{(24 - 2) \times 180^\circ}{24} = \frac{22 \times 180^\circ}{24} = \frac{3960^\circ}{24} = 165^\circ
     \]

These are the solutions and explanations for each part. Let me know if you'd like more details on any specific question, or if you have any further questions!

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Here are some related questions to deepen your understanding:

1. Why can't an equilateral triangle be a scalene triangle?
2. How would the triangle inequality change if we had different side lengths for the triangle?
3. What are the defining properties of a rhombus versus a square?
4. How can you prove that the radius of a regular hexagon is equal to its side length?
5. How would you calculate the exterior angle of a regular 24-sided polygon?

**Tip:** Remember that the sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

Solve the math problems provided on the worksheet, including true/false questions about triangles and polygons, calculating possible side lengths of a triangle, drawing various quadrilaterals, determining the radius of a hexagon, and using formulas to calculate angle measures in polygons.

Explore solutions to a geometry quiz covering triangle types, polygon angles, and properties of regular shapes. Learn about triangle inequality, calculating interior angles, and finding the radius of a hexagon with step-by-step explanations.

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