# math

posted by .

51. The ﬁgure below illustrates an isosceles right
triangle with legs of length 1, along with onefourth of a circle centered at the right-angle
vertex of the triangle. Using the result that
the shortest path between two points is a line
segment, explain why this ﬁgure shows that
2(squareroot of 2) <2

• math -

I see this is the second time you posted this.
Of course you realize that we can't see any diagram, but I think I can draw it from your description

First of all, you must have a typo.
Did you mean 2√2 < π ??
Since your statement of2√2 < 2 is false, (2√2 = appr. 2.8)

In the triangle let the hypotenuse be h
h^2 = 1^2 + 1^2 = 2
h = √2

the arc is (1/4)(2π) = π/2

then because of the straight between two points is always less than a curve between the same two points,
√2 < π/2
multiply by 2
2√2 < π

## Similar Questions

1. ### corollary to isosceles triangle theorem

how to prove 1)the measure of each angle of an equilateral triangle is 60. 2)the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Thanks. 1) The angles in any triangle have to add up …
2. ### geometry

the vertices of triangle ABC are A(1,7)B(9,3)C(3,1) a.prove that the triangle is a right triangle b.which angle is the right angle?

Which of the statements is ALWAYS TRUE? A-A right triangle is a scalene triangle. B-An equilateral triangle is an isosceles triangle. C-An isosceles triangle is an obtuse triangle. D-A right triangle is an acute triangle. I got either
4. ### geometry

The perimeter of right triangle RST is equal to the perimeter of isosceles triangle XYZ. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer. what is the greatest …
5. ### geometry

51. The ﬁgure below illustrates an isosceles right triangle with legs of length 1, along with onefourth of a circle centered at the right-angle vertex of the triangle. Using the result that the shortest path between two points …
6. ### Math (Geometry)

The perimeter of right triangle ABC is equal to the perimeter of isosceles triangle DEF. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer, what is the greatest …
7. ### Math

1) The hypotenuse of an isosceles right triangle is 8 cm longer than either of its legs. Note that an isosceles right triangle is a right triangle whose legs are the same length. Find the exact length of its legs and its hypotenuse. …
8. ### Math

Can someone please check to see if I answered these true and false statements correctly?
9. ### Math

1. the points given are two of the 3 vertices of a right triangle. Which could be the third vertex of the triangle given 2 points are (-4,-5) & (3,2) ?
10. ### math

Plane A which contains an isosceles right triangle forms a dihedral angle of 60 degrees with another plane B. If the hypotenuse of the triangle lies in plane B and measures 8 in., find the distance from the vertex of the right angle …

More Similar Questions