Please Help. Match the reasons to the statements given.
1 answer:
Answer:
1. Given
2. Diagonals of a parallelogram bisect each other.
3. Vertical angles are equal.
4. Definition of parallelogram.
5. If lines parallel, then alternate interior angles are equal.
6. ASA
7. CPCTE
Step-by-step explanation:
Statement 1:
The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.
Statement 2:
BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence,
Statement 3:
Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.
Statement 4:
A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, is because of the definition of a parallelogram.
Statement 5:
Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.
Statement 6:
The triangles BET and DFT are now congruent because:
i.Angle-
ii. Side -
iii. Angle -
Therefore, by ASA postulate the two triangles are congruent.
Statement 7:
As the two triangles are congruent, then their corresponding parts are also equal.
So, by CPCTE,
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Answer:
A. DEF where
and
.
Step-by-step explanation:
At first we must keep in mind that two triangles are similar when they have same angle configuration, that is, each pair of angles is congruent. If ABC and
DEF, then
and
. Hence,
and
.
In a nutshell, correct answer is A.
The volume of a cube (V) is given in terms of its side length (s) as
... V = s³
You have
... 27n²⁷ = s³
You may recognize that 27 = 3³, so this can be written as
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... 3n⁹ units