Pythagorean theorem - math word problems - page 41 of 67
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: 1340
- Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is the value of k? - Right-angled 82561
Determine point C so that triangle ABC is right-angled and isosceles with hypotenuse AB, where A[4,-6], B[-2,10] - Applies 14683
Point B is the center of the circle. The line AC touches the circles at point C and applies AB = 20 cm and AC = 16 cm. What is the radius of the circle BC? - Calculate 7214
Two tangents are drawn from point C to a circle with a radius of 76 mm. The distance between the two contact points is 14 mm. Calculate the distance of point C from the center of the circle.
- A circle 2
A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is r units. The point (-15, y) lies in this circle. What are r and y (or y1, y2)? - Determine
Determine which type of quadrilateral ABCD is and find its perimeter if you know the coordinates of vertices: A/2,4 /, B / -2,1 /, C / -2, -2 /, D/2, -5 /. - Perpendicular projection
Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Calculate 6
Calculate the distance of point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
- Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14 - Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try to calculate the lengths of all medians and all sides. - Calculate 83160
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Triangle 45671
Draw a right triangle with side a = 5 cm, c = 8 cm. The right angle is at vertex C. What is the size of side b? *
- Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x. - Circle - AG
Find the coordinates of the circle and its diameter if its equation is: x² + y² - 6x-4y=36 - 3d vector component
The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3? - Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates [- 14; 0]? - Vertices of a right triangle
Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle.
Do you have homework that you need help solving? Ask a question, and we will try to solve it.