Triangle Proportionality Theorem Calculator

FAQs

What is a true statement about a 45-45-90 triangle?

A true statement about a 45-45-90 triangle is that the hypotenuse length is √2 times the length of either leg. Let's explain why 👇 From the sine definition: sin(45°) = opposite/hypotenuse hypotenuse = (1/sin(45°)) × opposite hypotenuse = √2 × opposite As the opposite sides are the legs, and both sides are equal: hypotenuse = √2 × leg

What is the converse of the triangle proportionality theorem?

As for any theorem, we can state a converse for the triangle proportionality theorem: If a line divides two sides of a triangle proportionally, that line must be parallel to the third side.

How do I prove the triangle proportionality theorem?

To prove the triangle proportionality theorem, consider a triangle ABC with a line DE parallel to BC (image below) As parallel lines form congruent angles, then: ∠ADE ≅ ∠ABC and ∠AED ≅ ∠ACB From the AA similarity criteria: △ABC ~ △ADE As the triangles are proportional: AB/AD = AC/AE Using the denominator subtraction property: (AB - AD)/AD = (AC - AE)/AE As AB - AD = DB and AC - AE = EC, we can achieve the proof of the triangle proportionality theorem: DB/AD = EC/AE That's how you prove the triangle proportionality theorem!