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What else can I help you with?
How do you prove that the diagonals and either base of an isosceles trapezoid form an isosceles triangle?
Consider the isosceles trapezium ABCD (going clockwise from top left) with AB parallel to CD. And let the diagonals intersect at O Since it is isosceles, AD = BC and <ADC = <BCD (the angles at the base BC). Now consider triangles ADC and BCD. AD = BC The side BC is common and the included angles are equal. So the two triangles are congruent. and therefore <ACD = <BDC Then, in triangle ODC, <OCD (=<ACD = <BDC) = <ODC ie ODC is an isosceles triangle. The triangle formed at the other base can be proven similarly, or by the fact that, because AB CD and the diagonals act as transversals, you have equal alternate angles.
What is the different between equal angles and congruent angles?
Oh, dude, let me break it down for you. So, equal angles have the same measure, like they're twins or something, while congruent angles are basically the same angle just chilling in different places. It's like saying two people are equally tall versus being the exact same person in two different places. Cool, right?
How do you draw all possible distinct area models to represent factors of 120?
The task, as described, is extremely difficult since there may be area models for more than two factors at a time. However, taking only rectangular areas and so only 2 factors at a time: Find the smallest factor of 120 = B1. Let L1 = 120/B1. Draw a rectangle with length = L1 units and breadth = B1 units. Find the next larger factor of 120, B2. Let L2 = 120/B2. If L2 ≤ B2 then stop. Otherwise draw a rectangle with length = L2 units and breadth = B2 units. Do the next smallest factor, and so on.
Mother's Day calendar 1960 through 2009?
Mother's Day calendar 1960 through 2009 is as follows (not UK): 1960 - May 8 1961 - May 14 1962 - May 13 1963 - May 12 1964 - May 10 1965 - May 9 1966 - May 8 1967 - May 14 1968 - May 12 1969 - May 11 1970 - May 10 1971 - May 9 1972 - May 14 1973 - May 13 1974 - May 12 1975 - May 11 1976 - May 9 1977 - May 8 1978 - May 14 1979 - May 13 1980 - May 11 1981 - May 10 1982 - May 9 1983 - May 8 1984 - May 13 1985 - May 12 1986 - May 11 1987 - May 10 1988 - May 8 1989 - May 14 1990 - May 13 1991 - May 12 1992 - May 10 1993 - May 9 1994 - May 8 1995 - May 14 1996 - May 12 1997 - May 11 1998 - May 10 1999 - May 9 2000 - May 14 2001 - May 13 2002 - May 12 2003 - May 11 2004 - May 9 2005 - May 8 2006 - May 14 2007 - May 13 2008 - May 11 2009 - May 10
Why are all even number digit palindromes divisible by 11?
First, by induction it is shown that 102n-1 ≡ -1 (mod 11) for all natural numbers n (that is, all odd powers of 10 are one less than a multiple of 11.) i) When n = 1, then we have 102(1)-1 = 10, which is certainly congruent to -1 (mod 11). ii) Assume 102n-1 ≡ -1 (mod 11). Then, 102(n+1)-1 = 102n+2-1 = 102×102n-1 102 ≡ 1 (mod 11) and 102n-1 ≡ -1 (mod 11), so their product, 102×102n-1, is congruent to 1×(-1) = -1 (mod 11). Now that it is established that 10, 1000, 100000, ... are congruent to -1 (mod 11), it is clear that 11, 1001, 100001, ... are divisible by 11. Therefore, all integer multiples of these numbers are also divisible by 11. A palindrome containing an even number of digits may always be written as a sum of multiples of such numbers. The general form of such a palindrome, where all the As are integers between 0 and 9 inclusive, is A0 100 + A1 101 + ... + An 10n + An 10n+1 + ... + A1 102n + A0 102n+1 which may be rewritten as A0 (100 + 102n+1) + A1 (101 + 102n) + ... + An (10n + 10n+1) and again as 100 A0 (1 + 102n+1) + 101 A1 (1 + 102n-1) + ... + 10n An (1 + 101) Each of the factors in parentheses is one more than an odd power of 10, and is hence divisible by 11. Therefore, each term, the product of one such factor with two integers, is divisible by 11. Finally, the sum of terms divisible by 11 is itself divisible by 11. QED
If the diagonals of a parallelogram are congruent then the parallelogram may or may not be a rectangle. A.True B.False?
True because the diagonals of a rectangle are equal in lengths
The diagonals are congruent but the quadrilateral has no right angles is it a parallelogram?
No, a quadrilateral with congruent diagonals but no right angles is not necessarily a parallelogram. In order for a quadrilateral to be classified as a parallelogram, it must have both pairs of opposite sides parallel. The property of having congruent diagonals does not guarantee that the sides are parallel, so the quadrilateral may not be a parallelogram.
What type of parallelogram has 4 congruent angles but not necessarily 4 congruent sides?
:D I think that it is a rhombus cause a rhombus has four congruent sides but may not be a square or a rectangle.
Which group of quadrilaterals has diagonals that bisect their opposite angles?
Either a square or rectangle fit this description.
A parallelogram that has four congruent sides?
A parallelogram with four congruent sides may be either a square or a rhombus.
When can a parallelogram be a rectangle?
When all 4 corners are right angles. A parallelogram has two pairs of parallel sides. A rectangle has two pairs of parallel sides; therefore a rectangle is a parallelogram. A rectangle also has four 90° angles; a parallelogram does not necessarily have four 90° angles, therefore a parallelogram may, or may not, be a rectangle.
Are the diagonals of a kite equal in length?
From Wikipedia: '...a kite, or deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite.' In other words, a kite consists of two isosceles triangles joined at the base. Beginning with a particular isosceles triangle, it will always be possible to construct from it one kite that has equal diagonals (given that the kite may be either convex or concave). Hence an infinite number of kites do have equal diagonals, but many do not. A notable example of a kite that does have equal diagonals is a square.
What is a four-sided polygon with opposite sides equal and parallel?
A parallelogram. (A rectangle if the angles are 90o)A parallelogram (which may also be a rectangle, if all four angles are equal to 90°)
What is a parallelogram whose sides are equal in length?
A parallelogram whose sides are equal in length is always a rhombus. In addition, it may be a rectangle. If it's a rectangle, then it's also a square.
Does a parallelogram have congurent sides?
Its opposite sides are congruent. Its adjacent sides may be but it's not necessary. If they are, then it's a special kind of parallelogram, called a 'rhombus'.
What is difference in sides between a rectangle and a parallelogram?
The intersecting lines of a rectangle are at ninety degrees while the intersecting lines that form a parallelogram may be greater than or less than ninety degrees.
What has 4 side that are not equal?
A quadrilateral. It may be a rectangle, parallelogram, trapezoid, or an irregular quadrilateral.
