Question

In the figure 10.15, show that AB is parallel to CD, CD is parallel to EF and AB is parallel to EF . Justify your answer.

Answer 1

∠ABC=∠BCD......[ALTERNATE ANGLES]
Hence AB||CD
∠E+∠ECD=180
HENCE CD||EF
SINCE AB||CD AND CD||EF,
THEREFORE AB||EF

Answer 2

Answer:

Step-by-step explanation:

(i) From the figure, ∠ABC=40° and ∠BCD=20°+20°=40° and both of them are alternate to each other, hence AB║CD because two line segments are parallel if angles made by them form alternate angles pair.

(ii) Also, ∠FEC+∠ECD=160°+20°=180°, thus sum of corresponding angles is equal to 180°, then CD║EF.

(iii) Now, AB║CD and CD║EF, therefore AB║EF.

Hence proved.