Question

take the square root of both sides of the equation from part B (n↑2−c↑2=0) and write the resulting equation.

Answer 1

Part A

The equation for triangle 2 will be: a² + b² = n².

Part B

We know,

Now, we substitute a^2+b^2=c^2 in the second equation

So, the new equation is c^2 = n^2

Part C

Now, taking the square root of both sides of the equation from part B, we get

Part D

The equation obtained is true thanks to the Pythagorean theorem, because the corresponding legs in both triangles are of equal measure, we will obtain that their hypotenuse is also equal.

You can see that the 90° angles is conformed by 2 sides, these sides are the legs and the last side is the hypotenuse.

Part E

This means that the 2 triangles are equal, they have 3 sides equals.

The triangles also meet the criterion that explains that if two sides and the angle opposite the longest side are equal, the triangles are equal.

Part F

Yes, the triangle 1 is a rigth triangle because this has a right angle, that is, a 90 degree angle

Step-by-step explanation: Hope it helps!

Answer 2

Given:

A right angled triangle named as triangle 2 with sides perpendicular height(a),

base(b) and hypotenuse(n).

Required:

Find the resultant equation using two sides.

Step-by-step explanation:

By Pythagoras theorem we know that sum of square of base and perpendicular height of triangle equal square of hypotenuse.

Here, perpendicular height(a) and base(n)

`a^2+b^2=n^2`

This is the resulting equation.

Answer:

Hence, resulting equation is above.