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Brut [27]
3 years ago
6

If the diagonals of a quadrilateral bisect the angles, is the quadrilateral always a parallelogram? Explain your answer.

Mathematics
1 answer:
Liula [17]3 years ago
6 0
Yes. If the diagonals bisect the angles, the quadrilateral is always a parallelogram, specifically, a rhombus.


Consider quadrilateral ABCD. If diagonal AC bisects angles A and C, then ΔACB is congruent to ΔACD (ASA). Hence AB=AD and BC=CD (CPCTC).

Likewise, if diagonal BD bisects angles B and D, triangles BDA and BDC are congruent, thus AB=BC and AD=CD. (CPCTC again). Now, we have AB=BC=CD=AD, so the figure is a rhombus, hence a parallelogram.
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In a right triangle the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=3, b=4;
prohojiy [21]

Answer:

The hypotenuse is 5

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of a right triangle

a^2 +b^2 =c^2 where a and b are the legs and c is the hypotenuse

3^2 +4^2 =c^2

9+16=c^2

25=c^2

Take the square root of each side

sqrt(25) =sqrt(c^2)

5 = c


6 0
3 years ago
Read 2 more answers
9/17 15/34 6/17 9/34 geometric sequence?
zysi [14]
In a geometric sequence each number after the first is found by multiplying the previous number by a fixed number called the common ratio.

In an arithmetic sequence, each term is equal to the previous term plus or minus a constant called the common difference.

In your problem we have a sequence of numbers that appears to be decreasing in value, but on the surface it doesn't appear to be by any constant number... but if you look closely, the denominator 34 is exactly twice the other denominator 17. This would lead me to look at a common denominator to see if anything takes shape...

9/17 = 18/34
15/34
6/17 = 12/34
9/34

Now we see that each number is the previous number minus 3/34, so we have a common difference of 3/34.

This would match the definition of an arithmetic sequence and NOT a geometric sequence.
6 0
3 years ago
57000 x45 pls helppppppp​
Varvara68 [4.7K]

Answer:

2565000

Step-by-step explanation:

Easy, multiply them in a table.

3 0
3 years ago
Read 2 more answers
What is the value of x in the equation -2/3 x +9= 4/3x -3?
HACTEHA [7]

-2/3x+9=4/3x-3 original problem add 2/3x to both sides

9=6/3x-3 simplify 6/3 to 2 and add 3 to both sides

12=2x  divide both sides by 2

x=6

hope that helps



5 0
4 years ago
the rational roots of a polynomial function f(x) can be written in the form p/q where p is a factor of the leading corfficient o
Lorico [155]

False.

The Rational Root theorem states that P is a factor of the constant term and q is a factor of the leading coefficient.

4 0
3 years ago
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