Unit 7 - geometry & circle theorems

Question 1

State and briefly explain the 7 circle theorems

Answer 1

1. The angle in a semi-circle is 90 degrees (when one side of triangle is diameter)
2. The angle at the center is twice the angle at the circumference
3. Angles at the circumference from the same arc are equal
4. In a cyclic quadrilateral, in opposite angles up to 180 degrees
5. The angle between a tangent and a radius is 90 degrees
6. From any point you can only draw 2 tangents and they will be equal
7. Alternate segment theorem (angles between tangent and shape outside are equal to opposite angles in triangle)

Question 2

State 4 rules about angles in parallel lines

Answer 2

1. Alternate angles are equal (z shape)
2. Corresponding angles are equal (F shape_
3. Co-interior angles add up to 180 degrees
4. Vertically opposite angles are equal

Question 3

What happens to scale factors with area & volume?

Answer 3

Area - original scale factor squared
Volume - original scale factor cubed