Geometry Assignment

Task 1

Part A:

1. ABC is a right triangle because the measurement of angle C is 90 degrees.

2. Then segment AB is the hypotenuse of the triangle

3. By Pythagorean Theorem, AB^2 =AC^2 + BC^2

4. AB= square root[(AC)^2 + (BC)^2)]

5. The measurement of AC and BC is the distance from point A to C and the distance from point B to C, respectively.

6. Let A be the coordinates (X1,Y1); B(X2,Y2); C(X2,Y1)

7. With AC being a horizontal line segment both y-coordinates are the same. The measurement of AC would be (X2-X1)

8. With BC being a vertical line segment, the x-coordinates are the same. The measurement of BC would (Y2-Y1)

9. By substitution AC^2 = [(X2-X1)^2]; BC^2 = [(Y2-Y1)^2]

10. AB=square root[(X2-X1)^2) + (Y2-Y1)^2]

Part B:

1. ABD is a right triangle because the measurement of angle B is 90 degrees.

2. Then segment AD is the hypotenuse of the triangle

3. By Pythagorean Theorem, AD^2 = AB^2 + DB^2

4. As points A and B lie on the same plane, there Z-coordinates values are equal.

5. Let point A be denoted as coordinates (X1, Y1, and Z1) and point B be denoted as (X2, Y2, Z1)

6. As point D is in the same position, but a higher plane as B its coordinate system will be (X2, Y2, Z2) as the only difference in this point is its position on the Z-axis.

7. AD = Square root of [(X2-X1)^2 +(Y2-Y1)^2 + (Z2-Z1)^2]

8. The measurement of AB and DB is the distance from point A to B and point D to B, respectively.

9. With AB previously defined as square root[(X2-X1)^2 +(Y2-Y1)^2], still holds true taking in account the third dimension since it on the same plane with no change in the z-axis.

10. Since DB is a vertical line on the z-axis, its x and y coordinates are the same. The length of DB is given by it change on the z-axis of (Z2-Z1)

11. By substitution AB^2 = [(X2-X1)^2 +(Y2-Y1)^2]; DB^2 = [(Z2-Z1)^2]

12. AD = square root[(X2-X1)^2 + (Y2-Y1)^2 +(Z2-Z1)^2]

Using the...