Question

1. select the correct answer.

at least one diagonal in a(n)____polygon contains points in the exterior of the polygon.
equiangular
convex
concave
equilateral

1. select the correct answer.

none of the diagonals in a(n)____polygon contain points in the exterior of the polygon.
concave
convex
equilateral
vertices

Explanation:

• For the first question:
• An equiangular polygon has all angles equal. This property has no direct relation to the position of diagonal - exterior point relation.
• A convex polygon has all interior angles less than \(180^{\circ}\) and all diagonals lie inside the polygon.
• A concave polygon has at least one interior angle greater than \(180^{\circ}\). By the definition of a concave polygon, at least one of its diagonals will pass through the exterior of the polygon.
• An equilateral polygon has all sides equal. This property has no direct relation to the position of diagonal - exterior point relation.
• For the second question:
• A concave polygon has at least one diagonal that lies outside the polygon (as explained above).
• A convex polygon is defined as a polygon in which all interior angles are less than \(180^{\circ}\) and all diagonals lie within the interior of the polygon.
• An equilateral polygon has all sides equal. This property does not guarantee that diagonals lie inside the polygon.
• Vertices are the corner - points of a polygon, not a type of polygon.

Answer:

• 4. concave
• 5. convex