6. Let ABCD be a trapezoid with bases BC and AD. A line passing through the vertex C and parallel to the diagonal BD of ABCD intersects the line through the base AD at the point M. Prove the triangle A ACM has the same area as the trapezoid.

Q: Consider the triangle with vertices in the points D(-5,0,5), E(2, 1,3), and C(3, 1,4). Compute the…

A: Vertices of triangle D(-5, 0,5) , E(2, 1,3) and C(3, 1,4) . We have to compute the area of triangle…

Q: 56. Show that the six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1)…

A: Plotting given six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1).…

Q: 4. Show that the two internal bisectors and one external bisector of the angles of a triangle meet…

A: Given:

Q: 3. Let ABC be a triangle with D the midpoint of AB and E a point on AC so that DE is parallel to BC.…

A:

Q: 3. Let a = -i+ 3j + 2k and b = 4i + 5j+ 2k. Don’t evaluate the square roots for the lengths except…

A: Given that                    a→=-i^+3j^+2k^                     b→=4i^+5j^+2k^  We know that the…

Q: Example Give quadrilateral ABCD with verticesA(4, 7), B(8, 3), C(6,-1), andD(0, 5). Prove: ABCD is a…

A: Given : Quadrilateral ABCD with vertices A(4,7),B(8,3),C(6,-1) and D(0,5). So, Graph is :

Q: Show that a triangle with vertices at A(−1, 2), B(4, 1), and C(5, 6) is isosceles. Distance from…

A:

Q: Let vertices of an acute-angled triangle are A(z₁), B(z₂), and C(23). If the origin O is the…

A:

Q: (2, 3.5)

A: Here, the given function is,

Q: 10. What is the radius of the circle that has an area equal to that of the ellipse+¹=1 64

A: Follow the procedure given below.

Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

A:

Q: Consider a triangle with vertices X, Y, and Z.

A: Definition used -              Triangle law of vector addition -                  According to…

Q: AB²+ AC² = 2(AO² + BO²) e O is the middle point of BC.

A: Part A

Q: The triangle formed by A(z₁), B(z2) and C(z3) has its circumcentre at origin. If the perpendicular…

A:

Q: Compute the area of the triangle. T = = ||OP x oQ|| = |(36, -36, 36) || = II ト

A:

Q: 25. Prove analytically that the four diagonals joining opposite vertices of a rectangular…

A:

Q: Show that the triangle with vertices A(1, 2), B(-2, -1), and C(-4, 4) is isosceles. We must first…

A: Given: A(1, 2), B(−2, −1), and C(−4, 4)