Guided Geometry Questions

What is a quadrilateral? How is it different from a triangle or a pentagon?

• A four-sided flat shape; triangles have 3 sides, pentagons have 5.

• A shape with any number of sides; triangles and pentagons are special names.

• A shape with 4 curved sides; triangles and pentagons have straight sides.

• A shape with 4 equal sides; triangles and pentagons do not.

How many diagonals does any four-sided shape have? Can you draw them?

• Two diagonals; they connect opposite corners.

• One diagonal; it splits the shape into two equal parts.

• Three diagonals; each connects two non-adjacent corners.

• No diagonals; only triangles have diagonals.

Use a ruler: are any two sides perfectly parallel (never meet)? Use a set square: are any two sides perfectly at right angles (90°)?

• Parallel sides never meet; right angles look like an L-shape.

• Parallel sides cross at 90°; right angles are slanted.

• Parallel sides meet once; right angles never meet.

• Parallel sides can curve; right angles are only in triangles.

In a parallelogram, are opposite sides the same length? Are opposite angles the same size?

• Yes and yes.

• Yes sides same, angles different.

• No sides different, angles same.

• No and no.

Draw both diagonals in a parallelogram. Where they cross, what do you notice?

• They cross at their midpoints (they cut each other in half).

• They do not cross at all.

• They cross at one corner.

• They cross but not at equal lengths.

A rectangle is a parallelogram with all right angles. A rhombus is a parallelogram with all sides equal. How do their diagonals behave?

• Rectangle: diagonals equal but not perpendicular. Rhombus: diagonals perpendicular but not equal.

• Rectangle: diagonals perpendicular but not equal. Rhombus: diagonals equal but not perpendicular.

• Both have diagonals equal and perpendicular.

• Both have diagonals unequal and not perpendicular.

A square is both a rectangle and a rhombus. Fold a square along one diagonal. Do the two halves match?

• Yes, they match exactly.

• No, they are different sizes.

• Only if the square is very small.

• Only if the square is drawn with pencil.

A kite has two pairs of equal, adjacent sides. Which diagonal splits its equal angles?

• The diagonal that connects the ends of the unequal sides.

• The diagonal that connects the ends of the equal sides.

• Neither diagonal splits any angles.

• Both diagonals split angles equally.

In a trapezium, only one pair of sides is parallel. How do the base angles add up?

• Each pair of base angles on a parallel side adds to 180°.

• They always add to 90°.

• They add to the same as the non-parallel sides.

• They do not have any special sum.

Any four-sided shape has angles that add to 360°. How could drawing one diagonal show that?

• It splits the shape into two triangles; each triangle's angles add to 180°. 180° + 180° = 360°.

• It creates three triangles, and 3 × 180° = 360°.

• It splits into two squares, each 180°.

• It splits into four right angles of 90° each.