Point form would be (1,-2)
Use A.P
2nd term - 1st term =12 = d
first term = a
use this formula a+(n=1)d where n is the no. of term in sequence.
The median of the trapezoid is the average of the bases. If we draw the trapezoid that is being described in this item, we will deduce that AB and DC are the bases and EF is given to be the median.
For this item,
EF = (AB + CD) / 2
Part A:
EF = (15 + 11) / 2 = 13
Part B:
AB = 2EF - CD
AB = (2)(14) - 10 = 18
Part C:
18 = ((5n - 9) + (2n + 3))/2
18 = (7n - 6) / 2
n = 6
Part D:
2y + 4 = ((5y + 2) + (-3y + 8))/2
y = 1
EF = 2(1) + 4 = 6
AB = (5(1) + 2 = 7
AB = -3(1) + 8 = 5
Answer:
<u>Congruent pairs of triangles:</u>
ΔABD ≅ ΔDCB
- AB≅CD - given
- ∠ABD ≅ ∠CDB - given
- BD≅DB - common side
- SAS - two sides and the included angle
ΔABD ≅ ΔEFD - SAS
- AB≅EF - given
- ∠ABD ≅ ∠EFD - given
- ∠ADB ≅ ∠EDF - vertical angles
- AAS - two angles and non-included side
<u>By using the above two we can state that:</u>
ΔBDC ≅ ΔDFE - by ASA or SSS
because
- BD ≅ DF (corresponding parts)
- AD ≅ BC (corresponding parts)
- AD ≅ ED (corresponding parts)
- and therefore BC ≅ ED
<u>We can't prove that:</u>
- ΔAGD is congruent with any of the others as not enough information
There is one side and one angle and we can' t get two angles or two sides with included angle. Maximum we can get is SSA which doesn't guarantee the congruence.