One way to engage students in a geometry challenge is to display a triangle and ask them to identify its properties. For example, you could ask them to determine the measures of the angles, the lengths of the sides, and whether it is a right, acute, or obtuse triangle.

Once students have identified the properties of the triangle, challenge them to draw different shapes with similar properties. For example, they could draw a different triangle with the same angle measures but different side lengths, or a quadrilateral with the same number of sides but different angles.

Encourage students to discuss the relationships between the different shapes they have drawn. For example, they could talk about how changing the side lengths of a triangle affects the measures of the angles, or how adding an extra side to a quadrilateral changes its properties.

By engaging students in this geometry challenge, they will have the opportunity to apply their knowledge of geometric properties and explore the relationships between different shapes. This can help deepen their understanding of geometry concepts and develop their problem-solving skills.