Answer :
To determine the correct property of an isosceles right triangle, let’s begin by recalling some fundamental properties of this type of triangle.
An isosceles right triangle features:
1. Two equal sides, known as the legs.
2. One right angle (90 degrees) between these two equal legs.
3. Two equal angles of 45 degrees each.
In an isosceles right triangle with legs of length [tex]\(a\)[/tex]:
1. The legs are both equal, so the lengths of the two legs are the same.
2. By the Pythagorean theorem, the relationship between the legs and the hypotenuse (let's call it [tex]\(c\)[/tex]) is:
[tex]\[ c^2 = a^2 + a^2 \][/tex]
This simplifies to:
[tex]\[ c^2 = 2a^2 \][/tex]
Taking the square root of both sides gives us:
[tex]\[ c = \sqrt{2}a \][/tex]
This indicates that the hypotenuse ([tex]\(c\)[/tex]) is [tex]\(\sqrt{2}\)[/tex] times as long as either leg ([tex]\(a\)[/tex]).
Hence, the true statement about an isosceles right triangle is:
B. The hypotenuse is [tex]\(\sqrt{2}\)[/tex] times as long as either leg.
An isosceles right triangle features:
1. Two equal sides, known as the legs.
2. One right angle (90 degrees) between these two equal legs.
3. Two equal angles of 45 degrees each.
In an isosceles right triangle with legs of length [tex]\(a\)[/tex]:
1. The legs are both equal, so the lengths of the two legs are the same.
2. By the Pythagorean theorem, the relationship between the legs and the hypotenuse (let's call it [tex]\(c\)[/tex]) is:
[tex]\[ c^2 = a^2 + a^2 \][/tex]
This simplifies to:
[tex]\[ c^2 = 2a^2 \][/tex]
Taking the square root of both sides gives us:
[tex]\[ c = \sqrt{2}a \][/tex]
This indicates that the hypotenuse ([tex]\(c\)[/tex]) is [tex]\(\sqrt{2}\)[/tex] times as long as either leg ([tex]\(a\)[/tex]).
Hence, the true statement about an isosceles right triangle is:
B. The hypotenuse is [tex]\(\sqrt{2}\)[/tex] times as long as either leg.
