1. Find the measure of the unknown angles shown in the following diagrams and give the axiom or theorem used in each part. (Diagrams not to scale)
(i) A 80° (ii) 35° 70° B (iii)
110° D
(iv) E B D 145°
2. Contrails left by aircraft in the sky are shown in the picture.
Find the measure of the following angles shown in the picture and give the axiom or theorem used in each case.
(i) |∠Z| (ii) |∠X| (iii) |∠Y| [1AP11.16]
Z
120° X
Y
3. Look at the image of a pair of scissors. (i)
If the scissors are moved so that |∠A| = 30 ° , fi nd |∠B|
(ii) If the scissors are moved so that |∠A| = 100 ° , fi nd |∠C| (iii) If the scissors are moved so that |∠A| = 10 ° , fi nd |∠B| (iv) If the scissors are moved so that |∠B| = 10 ° , fi nd |∠D|
C D
4. (i) Use a ruler to draw two intersecting lines. (ii) Use a protractor to measure the four angles at the point where the lines intersect. (iii) What do you notice about the vertically opposite angles? (iv) Calculate the sum of the four angles. (v) Repeat parts (i) to (iv) two more times by drawing new lines.
5. Copy the table below and put a tick (✓) in the correct box in each row to show whether each statement is always true, sometimes true, or never true.
Statement
(i) A theorem is always correct. (ii) An axiom can be proven.
(iii) Vertically opposite angles are equal in measure.
(iv) A proof never has an end. Tick one box only for each statement Always true Sometimes true Never true