Question

Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
When m<1=m

Answer 1

Answer with explanation:

→If , AB ║ CD and AD  ║ BC

∠2 + ∠ D=180°----------(1)

→DA is a line.So, By linear pair

∠1 + ∠ 2=180°------------(2)

Equating (1) and (2)

∠1 + ∠ 2=∠2 + ∠D

Cancelling , ∠2 from both sides, gives

→∠1=∠D, is true statement.

You can also write Directly that, (∠1 and ∠D), and (∠3 and∠B), are corresponding angles, as lines are parallel,then corresponding angles are equal.

Answer 2

we know that

1) If the line segment AB is parallel to the line segment DC

then

m∠1=m∠D -------> by corresponding angles

2) If the line segment AD is parallel to the line segment BC

then

m∠3=m∠B -------> by corresponding angles