Which theorem proves ABC=DCB? Why?
1 answer:
Answer:
Parallel postulate : ALTERNATE INTERIOR ANGLES THEOREM.
Step-by-step explanation:
ALTERNATE INTERIOR ANGLES THEOREM : if a transversal cuts 2 parallel lines, then the alternate interior angles are said to be congruent.
( alternate interior angles : in the given figure, DCB and ABC are alternate interior angles.
ACB and CBD are another pair of alternate interior angles.)
[ theorem is an accepted truth or a verified correct statement already i.e, take protractor and measure it will be same in EVERY case. though i have provided the proof below..]
PROOF: since we know that vertically opposite angles will be congruent, so the angle vertically opposite to DCB will be same as DCB. ( refer attachment for vertically opposite angles) now, as corresponding angles will be congruent (see attachment to know what are corresponding angles), the angle vertically opposite to DCB and ABC are corresponding angles. therefore DCB and ABC are also equal
hence, ABC=DCB.
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Answer:
Width = 2x²
Length = 7x² + 3
Step-by-step explanation:
∵ The area of a rectangle is
∵ Its width is the greatest common monomial factor of and 6x²
- Let us find the greatest common factor of 14 , 6 and , x²
∵ The factors of 14 are 1, 2, 7, 14
∵ The factors of 6 are 1, 2, 3, 6
∵ The common factors of 14 and 6 are 1, 2
∵ The greatest one is 2
∴ The greatest common factor of 14 and 6 is 2
- The greatest common factor of monomials is the variable with
the smallest power
∴ The greatest common factor of and x² is x²
∴ The greatest common monomial factor of and 6x² is 2x²
∴ The width of the rectangle is 2x²
To find the length divide the area by the width
∵ The area =
∵ The width = 2x²
∴ The length = ( ) ÷ (2x²)
∵ ÷ 2x² = 7x²
∵ 6x² ÷ 2x² = 3
∴ ( ) ÷ (2x²) = 7x² + 3
∴ The length of the rectangle is 7x² + 3
Answer =44. Hope this answer is helpful and correct.
