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What is the relationship between right triangles and the areas of squares?
A right angle triangle with two side lengths that match that of an equivalent square will have exactly half the area of the square.
Why Does pythagorean theorem don't work for non right angle triangles?
The Pythagorean theorem specifically applies to right-angled triangles because it is based on the unique relationship between the lengths of the sides in such triangles. It states that the square of the length of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). In non-right triangles, this relationship does not hold, as the angles and side lengths do not conform to the theorem's criteria. Instead, the Law of Cosines is used for non-right triangles to relate their side lengths and angles.
Why does pythagorean theorem only work for right triangles?
The Pythagorean theorem applies specifically to right triangles because it defines a relationship between the lengths of the sides in a triangle where one angle is exactly 90 degrees. In this configuration, the lengths of the two legs (the sides forming the right angle) can be squared and summed to equal the square of the length of the hypotenuse (the side opposite the right angle). For triangles without a right angle, this relationship does not hold, as the properties of triangle geometry change, and the sum of the squares of the sides does not equal the square of the longest side. Thus, the theorem is uniquely suited to right triangles.
Are all right triangles congruent?
No, not all right triangles are congruent. Right triangles can have different side lengths and angles, as long as one angle is 90 degrees. Two right triangles are congruent if their corresponding sides and angles are equal, which is determined by criteria such as the Hypotenuse-Leg (HL) theorem or the Side-Angle-Side (SAS) criterion. Therefore, while some right triangles can be congruent, many others will not be.
Which congruence theorem guarantees that right angled triangles are congruent?
The checking for right-angled triangles is RHS:Right angle - they both haver a right angleHypotenuse - the hypotenuse of the triangles are congruentSide - a corresponding side of the triangles are congruent.
What is the relationship between right triangles and the areas of squares?
A right angle triangle with two side lengths that match that of an equivalent square will have exactly half the area of the square.
Why does pythagorean theorem only work for right triangles?
The Pythagorean theorem applies specifically to right triangles because it defines a relationship between the lengths of the sides in a triangle where one angle is exactly 90 degrees. In this configuration, the lengths of the two legs (the sides forming the right angle) can be squared and summed to equal the square of the length of the hypotenuse (the side opposite the right angle). For triangles without a right angle, this relationship does not hold, as the properties of triangle geometry change, and the sum of the squares of the sides does not equal the square of the longest side. Thus, the theorem is uniquely suited to right triangles.
What size and shape do two congruent triangles have?
to be congruent two triangles have, ASA-two angles the same with a side length between them. SAS-two side lengths the same and a same angle between them. SSS-all 3 side lengths the same. RHS-if the triangles are right angles ,and the hypotenuse are the same. :)
Are all right triangles congruent?
No, not all right triangles are congruent. Right triangles can have different side lengths and angles, as long as one angle is 90 degrees. Two right triangles are congruent if their corresponding sides and angles are equal, which is determined by criteria such as the Hypotenuse-Leg (HL) theorem or the Side-Angle-Side (SAS) criterion. Therefore, while some right triangles can be congruent, many others will not be.
How do you use two right angled triangles to make a parallelogram?
If they are congruent right angle triangles then just join them together side by side to form a parallelogram.
Which congruence theorem guarantees that right angled triangles are congruent?
The checking for right-angled triangles is RHS:Right angle - they both haver a right angleHypotenuse - the hypotenuse of the triangles are congruentSide - a corresponding side of the triangles are congruent.
How is hypotenuse represented in right triangles?
It is the largest side
Does the Pythagorean Theorem work on all triangles with side length of 1?
It doesn't matter on the side length, but it MUST have a right angle.
What is the relationship between the hypotenuse and a right angle?
The hypotenuse is the side opposite to the right angle in the triangle.
What shape is made out of two right triangles?
Two right triangles, when joined together by their hypotenuses (the side opposite the right angle), will form a rectangle.
What is true about the relationship among the three side lengths of any triangle?
A2+B2=C2A and B are the sides of a right triangle that aren't directly across the right angle. C is the hypotenuse. (This only applies to right triangles).Also, one that does pertain to all triangles is the well-known Law of Cosines, one used to develop the Pythagorean Theorem:c2 = a2 + b2 - abcos(A), where "c" is the hypotenuse, "b" is one side, "a" is another, and "A" is the angle on the opposite's side. (Between the opposite and the adjacent).
How do you make a triangle with 2 triangles and 1 rectangle?
If the 2 triangles are right triangles, which are congruent to slicing the rectangle on the diagonal, then arrange one on top of the rectangle, and the other to the side, so that the two hypotenuses are in line with each other. This will make a bigger right triangle, which is similar to the smaller right triangles - each side is double of the smaller triangles.
