Question

find the measure of EFGH if EFGH is a trapezium with EF II GH ​

Answer 1

Step-by-step explanation:

Given: EFGH is a trapezium with EF∣∣HG. Through X the mid-point of EH, is drawn parallel to EF.

To prove: XY bisects FG.

Construction: Join HF to intersect XY at P

In ΔHEF,XP∣∣EF (converse of mid-point theorem)

Therefore, XP bisects HF,PY∣∣HG ( as HY∣∣EF and EF∣∣HG)

ΔHGF,PY passes through mid-point of HF and is parallel to HG (converse of mid-point theorem)

Hence, XY bisects FG.

Answer 2

Given: EFGH is a trapezium with EF∣∣HG. Through X the mid-point of EH, is drawn parallel to EF.

To prove: XY bisects FG.

Construction: Join HF to intersect XY at P

In ΔHEF,XP∣∣EF (converse of mid-point theorem)

Therefore, XP bisects HF,PY∣∣HG ( as HY∣∣EF and EF∣∣HG)

ΔHGF,PY passes through mid-point of HF and is parallel to HG (converse of mid-point theorem)

Hence, XY bisects FG.