**Q5: **

The Pythagorean theorem states that, in a right triangle, the area of a square on the
hypotenuse is equal to the sum of the areas of the squares on the legs. Does this mean that a
triangle where is necessarily a right triangle?

Let us assume that is of side lengths , ,
and , with . Let be a right
triangle of side lengths , , and .

Using the Pythagorean theorem, what can you say about the relationship between
, , and ?

We know that for , .

What do you conclude about ?

Is it possible to construct different triangles with the same length sides?

What do you conclude about ?

**Q14: **

Two lines intersect at the point .
One line goes through the point ,
and the other goes through the point .

Find the lengths of , , and .

Using the Pythagorean theorem, decide: is triangle a right triangle?

Are the two lines perpendicular?

**Q15: **

Two lines intersect at the point .
One line goes through the point ,
and the other goes through the point .

Find the lengths of , , and

Using the Pythagorean theorem, decide: is triangle a right triangle?

Hence, are the two lines perpendicular?