12 multiple-choice questions, progressively harder.
Which description meets the polygon definition used here?
Solution
Correct answer: B
A polygon must be closed, made of straight sides, and simple.
Only the uncrossed closed straight chain meets all three conditions.
A polygon has seven vertices. What is its side-count name?
Correct answer: D
One boundary side leaves each vertex and reaches the next. Seven vertices therefore give seven sides.
A seven-sided polygon is a heptagon.
A simple quadrilateral is named ABCD in boundary order. Which segment is a diagonal?
Correct answer: A
A diagonal joins nonadjacent vertices. A and C are nonadjacent.
A and D are adjacent because the last side closes the boundary.
A simple polygon has an interior angle of 210 degrees. How is it classified?
Correct answer: C
An interior angle greater than 180 degrees is an inward, reflex corner.
This makes the simple polygon concave. It does not make its sides cross.
What does equilateral mean for a polygon?
Equilateral describes side lengths.
Equiangular describes angles, and regular requires both conditions.
A convex polygon is equiangular but has two unequal side lengths. Is it regular?
The angle condition holds, but the side condition fails.
A regular polygon must meet both.
Under the inclusive definition, which condition defines a trapezoid?
At least one parallel pair permits either one pair or two pairs.
A parallelogram therefore qualifies as a trapezoid.
Which name is guaranteed for a quadrilateral with both pairs of opposite sides parallel?
The two parallel pairs are precisely the parallelogram condition.
The other names need additional side or angle evidence.
Which pair of conditions defines a square within the parallelogram family?
Equal sides give the rhombus condition, and four right angles give the rectangle condition.
A square satisfies both.
For convex quadrilateral ABCD, which equal-side pairing directly satisfies the kite definition?
AB and AD meet at A, while BC and CD meet at C.
The two adjacent pairs are disjoint and use all four sides. Opposite pairs or a repeated side do not meet the definition.
An unmarked convex regular octagon has 8 sides. How many reflection axes does it have?
The reflection count of a convex regular polygon equals its side count.
The octagon has 8 axes: four through opposite vertices and four through opposite side midpoints.
An unmarked convex regular hexagon is tested for rotational symmetry. How many matching rotations are there, including identity once?
Each shift of the six vertices onto the next vertex positions gives one matching rotation.
There are six such positions, including the original identity position. A full turn repeats that position.
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