Answer:
The correct option is A.
Step-by-step explanation:
It is given that DEFG is a parallelogram.
Draw the diagonals DF and EG. Place point H where DF and EG intersect.
In triangle HGD and HEF
,
∠HGD ≅ ∠HEF (Alternate Interior angle)
∠HDG ≅ ∠HFE (Alternate Interior angle)
By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.
DG ≅ EF (Opposite sides of parallelogram)
According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.
So, by using ASA criterion for congruence we get,
ΔDGH ≅ ΔFEH
Since corresponding sides of congruent triangles are congruent, therefore
GH ≅ EH (CPCTC)
DH ≅ FH (CPCTC)
Option A is correct.
Answer:
each solo act will last 5 minutes and each ensemble act will last 14 minutes
Step-by-step explanation:
In the first show, we are told that there are 12 solo acts and 3 ensemble acts.
Now since each solo act lasts x minutes, and each ensemble act lasts y minutes and the show lasts 102 minutes, thus we have;
12x + 3y = 102 - - - - eq1
In the second show which lasts 72 minutes, we are told that there will be 6 solo acts and 3 ensemble acts.
Thus,we have;
6x + 3y = 72 - - - - eq2
Now, let's find x and y by subtracting eq 2 from eq1 to give;
6x = 30
Divide both sides by 6 to give;
x = 5
Put 5 for x in eq2;
6(5) + 3y = 72
30 + 3y = 72
3y = 72 - 30
3y = 42
y = 42/3
y = 14
Thus, each solo act will last 5 minutes and each ensemble act will last 14 minutes
Answer:
Step-by-step explanation:
so we search
hope this helps