Geometry Always/Sometimes/Never Quiz

Always Statements

• A square is classified as a rhombus, indicating all squares meet the properties of rhombuses.
• Perpendicular lines exist within the same plane, establishing a consistent geometric relationship.
• Two lines are defined as perpendicular if they form congruent adjacent angles, a key property in triangle and angle relationships.
• There is exactly one line perpendicular to a given line, passing through any external point, reinforcing concepts of parallel and perpendicular lines.
• A theorem has a definitive proof, demonstrating its validity within the mathematical framework.
• Two intersecting lines are always coplanar, confirming that they reside in the same plane.
• If points M and N are located on line PQ, and line segments PM and NQ are congruent, then line segments PN and MQ must also be congruent.

Sometimes Statements

• The diagonals of a parallelogram may bisect the angles, but this is not universally true for all parallelograms.
• A quadrilateral with one pair of congruent sides and one pair of parallel sides is sometimes classified as a parallelogram based on additional properties.
• The diagonals of a rhombus are sometimes congruent, not a defining characteristic of all rhombuses.
• A rectangle can have consecutive congruent sides, but not all rectangles will exhibit this property.
• The diagonals of a parallelogram being perpendicular bisectors is conditional and not an absolute truth.
• The exterior angle of a regular polygon can sometimes be less than the interior angle, depending on the configuration of the polygon.
• If two angles are supplementary to the same angle, they may or may not be supplementary to each other, depending on the specific angles involved.
• The converse of a theorem may occasionally hold true, but it is not guaranteed for all theorems.
• A rhombus can be a square, but not all rhombuses fulfill the additional criteria necessary for squareness.
• A parallelogram may also be a rectangle, depending on the angles being right angles.
• Supplementary angles can form a linear pair, but this is not a requirement for all supplementary angle pairs.

Never Statements

• A right triangle can never be equilateral, as equilateral triangles have all sides equal and angles of 60 degrees.
• The base of an isosceles triangle is never greater than the sum of its two legs, consistent with triangle inequality principles.
• If parallel lines are intersected by a transversal, the alternate interior angles will always be congruent, so they cannot be non-congruent.