A Tale of Three Intersecting Lines: common misconceptions

If your child says… “Angle CAB is at C.”

Ask together

Where does the path from C through A to B turn?

What’s true

The middle letter A identifies the corner of angle CAB.

If your child says… “Both circles must have the same radius.”

Ask together

Would equal compass openings give us both a 5 cm side and a 6 cm side?

What’s true

Each radius matches its required side, so the radii can differ.

If your child says… “The shorter sides just reach, so a triangle fits.”

Ask together

In the middle diagram, where could a third corner sit away from the base line?

What’s true

Equal total length leaves a flat line, with nothing enclosed.

If your child says… “These measurements could give different third sides.”

Ask together

Which endpoint could move while keeping all these measurements?

What’s true

Fixing both sides and their included angle fixes the remaining side.

If your child says… “A shorter base changes the third angle.”

Ask together

With both arm directions unchanged, what could change the angle where they meet?

What’s true

Changing the base length keeps the third angle unchanged when both base angles stay fixed.

If your child says… “A bigger triangle has a bigger angle total.”

Ask together

Would larger paper change the angle made by a straight line?

What’s true

Every triangle has the same angle total, regardless of its size.

If your child says… “The outside angle equals just one far corner.”

Ask together

What gap remains when you put only one torn corner there?

What’s true

The exterior angle combines both distant interior angles.

If your child says… “Every height must stay inside the triangle.”

Ask together

Can the card's perpendicular edge reach this vertex without extending the base?

What’s true

An altitude can meet an extended side outside the triangle.