Pythagorean theorem - math word problems - page 43 of 68
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:c2 = a2 + b2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
A common proof of the Pythagorean Theorem is called the "area proof". To prove the theorem using this method, we can create a square with side length c and two smaller squares with side lengths a and b, as shown in the figure. We can then place the smaller squares next to each other to form a rectangle with area a x b. We can then see that the area of the square with side length c is equal to the sum of the areas of the smaller squares, which is equal to the area of the rectangle. This demonstrates that c2 = a2 + b2, as stated in the theorem.
Another proof is Euclidean proof which is based on the Euclidean geometry and construction of a line segment that is c and perpendicular to the line segment of a and b.
Number of problems found: 1343
- Calculate 8
Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0. - Calculate 7
Calculate the height of the trapezoid ABCD, where the coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3] - Coordinates of square vertices
I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C and D. Thanks, Peter. - Midpoint of segment
Find the distance and midpoint between A(1,2) and B(5,5).
- Construct
Construct a rhombus ABCD if the size of the diagonal AC is 6 cm and the diagonal BD is 8 cm long. - Construct 5868
Construct a square if u-a = 1 - Determine 3586
Determine the size of the vectors u = (2,4) and v = (-3,3) - Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x; - Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
- Equation of circle
Find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16. - Square side
Calculate the length of the side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0. - Circumscribing
Find the radius of the circumscribed circle to the right triangle with legs 6 cm and 3 cm. - Equation of the circle
Find an equation of the circle whose diameter has endpoints (1,-4) and (3,2). - Vectors abs sum diff
The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|.
- Distance between 2 points
Find the distance between the points (7, -9), (-1, -9) - Medians and sides
Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6). - Equation 81932
Write the general equation of a circle with point S(2;5) and point B(5;6) lying on this circle. - Center
Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0 - Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5].
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