(i) Copy the diagrams of two parallel lines and a transversal. (ii) Mark in two pairs of corresponding angles (iii) Use a protractor to measure the corresponding angles. (iv) What do you notice about the corresponding angles?
(v) Repeat parts (i) to (iv) two more times with other pairs of parallel lines and transversals. What do you notice?
2. Using the diagram below, fi nd the measure of the following angles and give the theorem and/ or axiom used to fi nd the angle in each case (diagram not to scale).
B D
E A C
F G 134° ( i ) ( i i )
|∠A| |∠B|
( i i i ) |∠C| ( i v ) |∠D|
( v ) |∠E|
( v i ) |∠F| ( v i i ) |∠G|
95°
5. Below is map of Dungloe, Co. Donegal. R259 is parallel to Chapel Rd, and Caravan Rd is a straight road.
( a)
( b)
3. Using the diagram below, fi nd the measure of the following angles and give the theorem and/ or axiom used to fi nd the angle in each case (diagram not to scale).
58°
S P M N R O
Q ( i ) ( i i ) ( i i i )
|∠M| |∠N| |∠O|
( i v ) |∠P|
4. In each of the following diagrams, state whether each of the pairs of lines cut by the transversal are parallel or not, and give a reason for your answer.
( i ) 53° 53° ( i i ) 65° 67°
Find the following angles, and give the theorem and/or axiom used to justify your answer (diagram not to scale).
(i) |∠A| (ii) |∠B| (iii) |∠C| ( v ) |∠Q|
( v i ) |∠R| ( v i i ) |∠S|
( i i i )
78° 102°
( i v )
47° 133°
Section A Introducing concepts and building skills