Bisectors, loci and shading regions

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

A 110 degree angle is bisected. What is each part in degrees?
Answer: ______________
An 80 degree angle is bisected with compasses. What is each part?
- 40 degrees
- 80 degrees
- 20 degrees
- 160 degrees
An 80 degree angle is bisected with compasses. What is each part?
- 40 degrees
- 20 degrees
- 160 degrees
Sam says the locus of points exactly 3 cm from a point P is a circle of radius 3 centred at P. Is Sam right?
Circle one: True False
Points within 3 cm of a straight line form a strip. How wide is the strip in cm?
Answer: ______________
What is the locus of points a fixed distance from a line segment?
- A full circle
- A single parallel line
- A stadium shape
A perpendicular bisector is drawn for A(2, 4) and B(6, 8). Which point lies on it?
- (5, 5)
- (4, 4)
- (4, 6)
- (8, 12)
Maya says construction arcs must be left visible as evidence of method. Is Maya right?
Circle one: True False
A 136 degree angle is bisected, then one half is bisected again. What is the final piece in degrees?
Answer: ______________
A 136 degree angle is bisected, then one half is bisected again. What is the final piece in degrees?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

55 · 110 over 2 = 55.
40 degrees · Half of 80 is 40. The 20 option quarters instead of halving.
40 degrees · Half of 80 is 40.
True · Fixed distance from one point defines a circle.
6 · 3 cm each side gives 3 + 3 = 6.
A stadium shape · Strips along the straight part plus semicircles round the ends.
(4, 6) · Midpoint: x = (2+6)/2 = 4, y = (4+8)/2 = 6. The (8, 12) option adds instead of averaging.
True · Examiners award construction marks for the arcs themselves.
34 · 136 over 2 is 68, then 68 over 2 is 34.
34 · 136 over 2 = 68, then 68 over 2 = 34.