Question

Точка К не лежить у площині квадрата АВСД. Доведіть що АВ || (СКД)

Answer 1

Problem Statement

You are given a square ABCD, and you need to prove that line segment AB is parallel to line segment SKD.

Solution

To prove that line segment AB is parallel to line segment SKD, we need to show that the slopes of these two lines are equal.

Let's assume that point A has coordinates (x1, y1), point B has coordinates (x2, y2), point S has coordinates (x3, y3), point K has coordinates (x4, y4), and point D has coordinates (x5, y5).

The slope of line AB can be calculated using the formula: m1 = (y2 - y1) / (x2 - x1)

The slope of line SKD can be calculated using the formula: m2 = (y4 - y3) / (x4 - x3)

If the slopes of these two lines are equal, then line segment AB is parallel to line segment SKD.

Let's calculate the slopes of these two lines and compare them:

Slope of AB (m1): Using the coordinates of points A and B, we can calculate the slope of line AB.

Slope of SKD (m2): Using the coordinates of points S, K, and D, we can calculate the slope of line SKD.

If m1 = m2, then line segment AB is parallel to line segment SKD.

Please provide the coordinates of points A, B, S, K, and D, and I will calculate the slopes and verify if AB is parallel to SKD.