Respuesta :
1. prove: in a 45°–45°–90° triangle, the hypotenuse is [tex] \sqrt{2} [/tex] times the length of each leg.
2. ecause triangle xyz is a right triangle, the side lengths must satisfy the pythagorean theorem,[tex] a^{2} + b^{2}= c^{2}[/tex] , which in this isosceles triangle becomes [tex] a^{2} + a^{2}= c^{2}[/tex]
3. By combining like terms: [tex] 2a^{2}= c^{2}[/tex]
4. Determine the principal square root of both sides of the equation:
[tex] \sqrt{2a^{2}} = \sqrt{c^{2}} [/tex]
[tex]\sqrt{2} a=c[/tex]
5. So the hypothenuse c is [tex] \sqrt{2} [/tex] times the length of each leg a.
2. ecause triangle xyz is a right triangle, the side lengths must satisfy the pythagorean theorem,[tex] a^{2} + b^{2}= c^{2}[/tex] , which in this isosceles triangle becomes [tex] a^{2} + a^{2}= c^{2}[/tex]
3. By combining like terms: [tex] 2a^{2}= c^{2}[/tex]
4. Determine the principal square root of both sides of the equation:
[tex] \sqrt{2a^{2}} = \sqrt{c^{2}} [/tex]
[tex]\sqrt{2} a=c[/tex]
5. So the hypothenuse c is [tex] \sqrt{2} [/tex] times the length of each leg a.
The hypotenuse is [tex]\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the pythagorean theorem becomes [tex]a^2 = c^2[/tex] and this can be evaluated by using poperties of isosceles triangle.
Given :
Isosceles triangle XYZ where [tex]\rm \angle X = 45^\circ,\;\angle Y = 45^\circ,\;\angle Z = 90^\circ[/tex].
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a. Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now, applying pythagorean theorem on triangle XYZ.
[tex]\rm a^2+b^2 =c^2[/tex]
Here, a = b because XYZ is an isosceles triangle.
[tex]\rm a^2+a^2=c^2[/tex]
[tex]\rm 2a^2 = c^2[/tex]
[tex]\rm a\sqrt{2} = c[/tex]
Therefore, it can be concluded that the hypotenuse is [tex]\sqrt{2}[/tex] times the length of each leg 'a'.
For more information, refer the link given below:
https://brainly.com/question/24252852
