How to name a triangle when two sides are equal and one pair of sides is parallel

Expert intro: This is a straightforward geometry identification question. The key clue is the equality of two sides in the same triangle.

Detailed walkthrough

We are told that in triangle $ABD$,

$AB=AD.$

A triangle with two equal sides is called an isosceles triangle.

So the mathematical name of triangle $ABD$ is:

$\boxed{\text{isosceles triangle}}$

If you want to be a little more precise, $AB$ and $AD$ are the equal sides, so $BD$ is the base.

💡 Pitfall guide

Do not get distracted by the tangent or the parallel lines if the question only asks for the name of triangle $ABD$. The only information you need is $AB=AD$.

🔄 Real-world variant

If the problem had also stated that $AB=BD$, then triangle $ABD$ would be equilateral, not just isosceles. If only one pair of angles were equal, that would not be enough to name the triangle by side lengths.

🔍 Related terms

isosceles triangle, equal sides, triangle classification