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How do you prove that a hypotenuse of a right triangle is the side of greatest measure?
Wiki User
∙ 12y ago
For example, you can take a look at the Pythagorean formula: c = square root of (a2 + b2).
Wiki User
∙ 12y ago
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What does Hypotenuse-Leg mean?
"Hypotenuse-Leg" is a short-hand label for a corollary that you can use to prove that two right triangles are congruent. In general, in order to prove that two triangles are congruent, you have to show that either (two sides and the included angle) or (two angles and the included side) of one triangle are equal to the corresponding parts of the other one. But if you're dealing with two right triangles, it's enough to show that the hypotenuse and one leg of the the first triangle are equal to the hypotenuse and leg of the other one, and then you can say that the triangles are congruent. This process is called "Hypotenuse-Leg".
How do you prove pythagorean theorom?
The law of cosines states that in any triangle, c2 = a2 + b2 - 2abcosy, where c is the hypotenuse, a and b are the legs, and y is the angle opposite c, the hypotenuse. Since in a right triangle, this is always 90 degrees, the cosine of y will always be 0. since 2ab(0) is 0, we get the formula a2 + b2 = c2, the Pythagorean Theorem.
How to prove an isosceles triangle with one angle bisector?
What have we got to prove? Whether we have to prove a triangle as an Isoseles triangle or prove a property of an isoseles triangle. Hey, do u go to ALHS, i had that same problem on my test today. Greenehornet15@yahoo.com
What are four ways you can prove two right triangles are congruent?
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Does pythagorean theorem prove a triangle to be a right triangle?
Yes
How do you prove the pythagorean theorem?
For any right angle triangle its hypotenuse when squared is equal to the sum of its squared sides.
Can you show how a right triangle has one line of symmetry?
the only way for a right triangle to have a line of symmetry, is if the legs of the triangle are congruent. Or you can show that both non-right angles are congruent (45 degrees). you may also prove that the altitude of the triangle bisects the hypotenuse or that it equals 1/2 of the hypotenuse.
Prove that the the line segment joining the midpoint of the hypotenuse of a right triangle to the vertex of the right angle is equal to half the hypotenuse?
Simply by measuring it. Or by drawing a circle with a radius of half the hypotenuse and having the vertex of the right angle as its centre and if the midpoint of the hypotenuse just touches the circle then this proves it.
What does Hypotenuse-Leg mean?
"Hypotenuse-Leg" is a short-hand label for a corollary that you can use to prove that two right triangles are congruent. In general, in order to prove that two triangles are congruent, you have to show that either (two sides and the included angle) or (two angles and the included side) of one triangle are equal to the corresponding parts of the other one. But if you're dealing with two right triangles, it's enough to show that the hypotenuse and one leg of the the first triangle are equal to the hypotenuse and leg of the other one, and then you can say that the triangles are congruent. This process is called "Hypotenuse-Leg".
Why are there so many ways to prove the pythagorean theorem?
Because in a right angle triangle the square of its hypotenuse is always equal to the sum of each side squared.
Can a right angled triangle be equilateral?
No it can never be. Because the hypotenuse has to be the longest side and also square of hypotenuse should equal to sum of squares of other two sides. so if anyone finds a way to prove that 1=2 , the right angled triangle can be equilateral. Lets just wait and watch.
How do you make models for demonstrating trigonometry?
For example you can cut out a 3 inch base, 4 inch height and a 5 inch hypotenuse of a right angle triangle to prove Pythagoras' theorem that the hypotenuse squared is equal to the sum of its squared sides:- 32+42 = 52
How do you prove that a triangle is a right triangle?
all the angles add up to 180 degreespythagorean theorem. if it works, you have a right angle triangle. a^2 + b^2 = c^2. the sum of the squares of the two shorter sides is equal to the square of the longest side, also known as the hypotenuse.
How do you prove pythagorean theorom?
The law of cosines states that in any triangle, c2 = a2 + b2 - 2abcosy, where c is the hypotenuse, a and b are the legs, and y is the angle opposite c, the hypotenuse. Since in a right triangle, this is always 90 degrees, the cosine of y will always be 0. since 2ab(0) is 0, we get the formula a2 + b2 = c2, the Pythagorean Theorem.
How to prove an isosceles triangle with one angle bisector?
What have we got to prove? Whether we have to prove a triangle as an Isoseles triangle or prove a property of an isoseles triangle. Hey, do u go to ALHS, i had that same problem on my test today. Greenehornet15@yahoo.com
How can you prove that the is the sum of the lengths of any two sides of a triangle always greater than the length of the third one?
Simply measure them.
What are four ways you can prove two right triangles are congruent?
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
