Statement Reason
2 answers:
Answer:
D. Line segment BC is congruent to line segment AD.
Step-by-step explanation:
Given ABCD is a rectangle
AB=CD and BC= AD
1.Statement: ABCD is a rectangle.
Reason: Given
2.Statement: Line segment AB and line segment CD are parallel
Reason: By definition of parallelogram
3.Statement : Line segment AD and line segment BC are parallel
Reason: By definition of parallelogram
4.Statement:
Reason: Alternate interior angles theorem
5. Statement:
Reason: Alternate interior angles theorem.
6. Statement :Line segment BC is congruent to line segment AD
7.Statement:
Reason: Angle-Side_ Angle (ASA)
postulate
8.. Statement: Line segment BE is congruent to line segment DE
Reason: CPCT
9. Statement: Line segment AE is congruent to line segment CE
Reason: CPCT
10. Statement: Line segment AC bisects line segment BD
Reason: By definition of a bisector
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It will take exactly 4 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees:
- Type A is 3 feet tall and grows at a rate of 7 inches per year
- Type B is 5 feet tall and grows at a rate of 1 inches per year
We need to find in how many years it will take for these trees to be the
same height
Assume that it will take x years for these trees to be the same height
The height of a tree = initial height + rate of grow × number of years
Type A:
∵ The initial height = 3 feet
∵ 1 foot = 12 inches
∴ The initial height = 3 × 12 = 36 inches
∵ The rate of grows = 7 inches per year
∵ The number of year = x
∴ = 36 + (7) x
∴ = 36 + 7 x
Type B:
∵ The initial height = 5 feet
∴ The initial height = 5 × 12 = 60 inches
∵ The rate of grows = 1 inches per year
∵ The number of year = x
∴ = 60 + (1) x
∴ = 60 + x
Equate and
∴ 36 + 7 x = 60 + x
- Subtract x from both sides
∴ 36 + 6 x = 60
- Subtract 36 from both sides
∴ 6 x = 24
- Divide both sides by 6
∴ x = 4
∴ The two trees will be in the same height in 4 years
It will take exactly 4 years for these trees to be the same height
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