Parallel and Intersecting Lines: common misconceptions

If your child says… “The opposite angle must add to 180° with this one.”

Ask together

What remains when you subtract the same neighbour from each straight angle?

What’s true

Opposite angles have equal sizes.

If your child says… “Slanting lines cannot be perpendicular.”

Ask together

Did turning the sheet open or close any angle?

What’s true

The angle determines perpendicularity, not the sheet's direction.

If your child says… “These short pieces don't touch, so they must be parallel.”

Ask together

What would happen farther along if the gap kept shrinking?

What’s true

Separate pieces can belong to lines that meet beyond their ends.

If your child says… “Each fold doubles the number of boundary lines.”

Ask together

Count each strip's left boundary from left to right. Which outside boundary remains uncounted?

What’s true

Halving doubles the strips; their boundaries number one more.

If your child says… “Five different sizes should be possible.”

Ask together

How many sizes remain when you pair the opposite angles at each crossing?

What’s true

Each crossing contributes no more than two angle sizes.

If your child says… “Matching positions always mean equal angles.”

Ask together

Could both traced edges fit if the lower line sloped differently?

What’s true

These positions have equal angles exactly when the crossed lines are parallel.

If your child says… “These inside angles must add to 180°.”

Ask together

If a and b both match c, how do their sizes compare?

What’s true

Inside parallel lines, alternate angles have matching sizes.

If your child says… “The two inside angles on this side are equal.”

Ask together

Which angle equals a and also fills a straight angle with b?

What’s true

Their sizes total 180°; they match only when both are right angles.