Question

Given: L is the midpoint of AB TA is parrelell to CL; TL is parrelell to CB
Prove: angle ATL = angle LCB

Answer 1

Question

1) TL is parallel to CB. So, if CL intersects TL and CB, then the angle TLC equal to angle LCB. We have:

$$\angle TLC = \angle LCB$$

.

2) AT is parallel to LC. So, if TL intersects AT and LC, then the angle ATL is equal to the angle TLC. We have:

$$\angle ATL = \angle TLC$$

.

3) We have:

$$\left\{ \begin{array}{l} \angle TLC = \angle LCB \\ \angle ATL = \angle TLC \end{array} \right. \Rightarrow \angle ATL = \angle LCB$$

. Proved.

Answer: Proved.