Angles and line segments

Angles and line segments

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about using geometric properties to explain why line segments are the same length.
The centre of this circle is marked with a dot.
circle and line segment diagram
[Not drawn to scale]  

Question 2Change answer

a)  The line segments OA and OB are the same length.
     Explain why.
     

Question 2Change answer

b)  i)  What is the size of the shaded angle marked 'z'?  degrees
 
      ii) The line segments DB and AB are the same length.
          Explain why.
         
Task administration: 
This task can be completed with pen and paper or online (with NO auto marking).
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
angles, circles, line segments, tangents, radius, triangles, isosceles
Description of task: 
Students use the angle between a tangent and a radius property and the base angles in an isosceles triangle property to find an unknown angle and to explain why line segments are of equal size.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (10/1998)
a)   They are both radii of the same circle/middle point of circle. moderate
b) i)
ii)		 30°
Triangle BAD is an isosceles
(angle BDA = angle DAB).		 difficult
very difficult