Geometry Two Truths and a Lie

Which is the lie?

• The shape has at least one set of parallel sides

• The shape is a parallelogram

• The shape is a polygon

Answer explanation

Parallelograms are quadrilaterals with exactly two pairs of parallel sides. This shape is a hexagon.

Which is the lie?

• This is an equilateral triangle

• The shape has at least 1 acute angle

• The shape has at least one obtuse angle

Answer explanation

Equilateral triangles have 3 acute angles.

Which is the lie?

• Lines AB and CD are intersecting

• Lines AB and CD are parallel

• Lines AB and CD are perpendicular

Answer explanation

Perpendicular lines are a special type of intersecting lines that form right angles. Parallel lines will never touch or intersect.

Which is the lie?

• This is a quadrilateral

• This is a trapezoid

• This is a parallelogram

Answer explanation

Trapezoids are quadrilaterals with one pair of parallel sides. Parallelograms are quadrilaterals with two pairs of parallel sides.

Which is the lie?

• This shape has at least one obtuse angle.

• This shape is a pentagon.

• This shape has at least one pair of parallel lines.

Answer explanation

This is a pentagon, it has 5 sides. This pentagon does not have any parallel sides.

• This shape is a rhombus.

• This shape is a rectangle.

• This shape is a trapezoid.

Answer explanation

A square is considered a rhombus because it has 4 congruent sides and a rectangle because it has 4 right angles. A square is NOT a trapezoid because it has 2 pairs of parallel sides, not just one.

Which is the lie?

• This angle is acute.

• This angle could be about 50 degrees.

• This angle could be about 5 degrees.

Answer explanation

This acute angle is much larger than 5 degrees. It appears to be larger than 45 degrees.

Which is the lie?

• This is an equalateral triangle.

• This is a right triangle.

• This is a scalene triangle.

• Line AB and CD are congruent.

• Lines AB and CD are parallelograms.

• Lines AB and CD are paralell.

Answer explanation

These lines are parallel and congruent. They are not parallelograms because they are not polygons. Parallelograms have 4 sides and two sets of parallel lines.

Which is the lie?

• The shape has one line of symmetry.

• The shape has at least one pair of congruent sides.

• The shape has at least one right angle.

Answer explanation

The shape is known as a kite. Kites have two pairs of congruent adjacent sides. Kites do not have any parallel sides or right angles.