Triangles: common misconceptions

If your child says… “Their corners match, so all these rectangles are similar.”

Ask together

Does the 4 by 3 rectangle multiply both original dimensions by the same amount?

What’s true

Matching corners alone cannot establish polygon similarity; matching side lengths must also scale together.

If your child says… “AB can match whichever side is at the bottom.”

Ask together

After turning the triangle, which side still joins P to Q?

What’s true

Turning a triangle changes its position, while its matching vertices remain the same.

If your child says… “A parallel line always cuts both sides into halves.”

Ask together

What is the ratio of the lengths above and below DE on each side?

What’s true

A parallel cut halves both sides only when it passes through a midpoint.

If your child says… “Nearly equal ratios are enough to prove the lines parallel.”

Ask together

Would a nearby point still divide AC in exactly the required ratio?

What’s true

The converse requires exactly equal ratios, even when a drawing looks convincing.

If your child says… “BPT works directly on the whole trapezium.”

Ask together

Which triangle connects the left side to the diagonal, and which connects the right?

What’s true

The diagonal supplies two triangles, and each contributes a ratio needed for the conclusion.

If your child says… “Two matching angles aren't enough.”

Ask together

What room is left for different third angles after subtracting the same two angles?

What’s true

Matching two angles forces the third to match because every triangle totals 180°.

If your child says… “For perimeters, I square the side ratio.”

Ask together

If every side doubles, what happens when you add the three lengths?

What’s true

Adding side lengths preserves their common scale factor, so perimeter uses the unsquared ratio.