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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Parallel and Perpendicular lines

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Equation of a straight line for KS4
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:parallel_and_perpendicular_lines/3577/


Example 1.

Given the points , , and . Show that the given points are indeed vertices of a parallelogram.

    
Example 2.

For what value of b are the lines and parallel?

    
3.

The edges of the cuboid ABCDEFGH define the following geometric elements:


  • plane ,

  • plane ,

  • the line p,

  • the line q.


The following relationships apply between the elements:


  • The plane passes through the points C, D and H.

  • The plane passes through the points A and E and is perpendicular to the plane .

  • The line p represents the intersection of the planes and .

  • The line q lies on the plane and intersects the line p at the point D at a right angle.


Substitute the above four geometric elements correctly in the cuboid and write down the relationships between them with symbols.

    
4.

Write the relationships between the geometric elements in the diagram below:

  • point H,

  • the line p,

  • planes and

  • planes .


    
5.

In the room we have the following elements, as shown in the diagram below:




Check the correctness of the following statements:
















    
6.

The edges of the cuboid ABCDEFGH define the following geometric elements:

  • the line q,

  • planes and

  • planes .


The following relationships apply between the elements:

  • The plane passes through points A, C and D.

  • The plane has points A and D in common with the plane , and also passes through the point E.

  • The line q is perpendicular to the plane and passes through the point B.


Substitute the above three geometric elements correctly in the cuboid and write down the relationships between them with symbols.

    
7.

Write the relationships between the geometric elements in the diagram below:

  • the line p,

  • the line q,

  • the line r and

  • planes .


    
8.

In the room we have the following elements, as shown in the diagram below:




Check the correctness of the following statements:















    

9.

The edges of the cuboid ABCDEFGH define the following geometric elements:

  • plane ,

  • the line p,

  • the line q and

  • the line r.


The relationships between the elements are:

  • The plane passes through points A, D and H.

  • The line p passes through the point D and is perpendicular to the plane .

  • The line r passes through the point H and is perpendicular to the line p.

  • Line q passes through point E and is perpendicular to line r.


Substitute the above four geometric elements correctly in to the cuboid and write the relationships between them using symbols.

    
10.

Write the relationships between the geometric elements in the diagram below:

  • point A,

  • the line p,

  • the line q and

  • line r


    
11.

In the room we have the following elements, as shown in the diagram:




Check the correctness of the following statements:














    
12.

The edges of the cuboid ABCDEFGH define the following geometric elements:

  • the line p,

  • the line q and

  • the line r.


The relationships between the elements are:

  • The line q passes through the points A and D.

  • Line p passes through point B and is perpendicular to line q.

  • Line r is parallel to line p and intersects line q at point D.


Substitute the above three geometric elements correctly in to the cuboid and write the relationships between them using symbols.

    
13.

We have the following items in the room as shown in the diagram. Line p passes through points A and C, and line q passes through B and H.




Check the correctness of the following statements: