Question

Activityin this activity you will apply the converse of the Pythagorean Theorem to determine whether triangle BCD is a right triangle.B046.emDQuestion 1The first step is to find the missing side length in the diagramPart AAccording to the diagram, which triangle is a right triangle

Answer 1

Given:

The figure with some sides measurements.

Required:

What is missing side length and which triangle is a right triangle?

Explanation:

Converse of Pythagoras theorem:

$\begin{gathered} \text{ If the length of a triangle is }a,b\text{ and }c\text{ and }c^2=a^2+b^2,\text{ then the triangle} \\ \text{ is a right angle triangle.} \end{gathered}$

So, take BAD right triangle,

$\begin{gathered} BA^2+AD^2=BD^2 \\ 4^2+4^2=BD^2 \\ BD^2=16+16 \\ BD^2=32 \\ BD=4\sqrt{2} \end{gathered}$

Now,

$\begin{gathered} \text{ In }\Delta CBD, \\ BC^2+BD^2=CD^2 \\ 2^2+(4\sqrt{2})^2=6^2 \\ 4+32=36 \\ 36=36 \end{gathered}$

Answer:

$\begin{gathered} \text{ In diagram missing length equals }4\sqrt{2}\text{ and }\Delta BAD\text{ and }\Delta CBD\text{ are right} \\ triangles. \end{gathered}$