Quadrilateral $CDEF$ is a parallelogram. Its area is $36$ square units. Points $G$ and $H$ are the midpoints of sides $CD$ and $EF,$ respectively. What is the area of triangle $CDJ?$
+981 \(\because \angle DHE=\angle FHJ \) (vertical angles)
\(\because EH=HF\) (midpoint)
\(\because \overline{DE}\parallel\overline{FJ} \Rightarrow \angle EDJ =\angle FJD\) (alternating interior angles)
\(\therefore \triangle HDE\cong\triangle HJF\) (AAS Congruency)
\(\therefore [HDE]=[HJF] \Rightarrow [CDHF]+[HDE]=[CDHF]+[HJF]\)
\([CDJ]=[CDEF]\)
\(\boxed{36}\)
I hope this helped,
Gavin.
+981 \(\because \angle DHE=\angle FHJ \) (vertical angles)
\(\because EH=HF\) (midpoint)
\(\because \overline{DE}\parallel\overline{FJ} \Rightarrow \angle EDJ =\angle FJD\) (alternating interior angles)
\(\therefore \triangle HDE\cong\triangle HJF\) (AAS Congruency)
\(\therefore [HDE]=[HJF] \Rightarrow [CDHF]+[HDE]=[CDHF]+[HJF]\)
\([CDJ]=[CDEF]\)
\(\boxed{36}\)
I hope this helped,
Gavin.
