A quadrilateral has one pair of parallel sides, №12044091, 13.10.2020 18:46

Mathematics

Aquadrilateral has one pair of parallel sides with lengths 1 3/4 inches and 1 1/4 inches, and two angles that measure 36 degrees. what is the mane of the quadrilateral you drew?

Step-by-step answer

P Answered by PhD

14

The name of the quadrilateral is isosceles trapezoid.

Explanation:

1) The two parallel sides of different legths $1\frac{3}{4}$ and $1\frac{1}{4}$ constitute the bases of a trapezoid.

2) The two equal anglesare the base angles of the trapezoid, and mean that it is an isosceles trapezoid.

An isosceles trapezoid is truncated isosceles triangle.

The definition of trapezoid is a quadrilateral with at least two parallel sides.

The drawing is attached: only the green lines represent the figure, the dotted lines just show how this is derived from an isosceles triangle.

Mathematics

Aquadrilateral has one pair of parallel sides with lengths 1 3/4 inches and 1 1/4 inches, and two angles that measure 36 degrees. what is the mane of the quadrilateral you drew?

Step-by-step answer

P Answered by PhD

14

The name of the quadrilateral is isosceles trapezoid.

Explanation:

1) The two parallel sides of different legths $1\frac{3}{4}$ and $1\frac{1}{4}$ constitute the bases of a trapezoid.

2) The two equal anglesare the base angles of the trapezoid, and mean that it is an isosceles trapezoid.

An isosceles trapezoid is truncated isosceles triangle.

The definition of trapezoid is a quadrilateral with at least two parallel sides.

The drawing is attached: only the green lines represent the figure, the dotted lines just show how this is derived from an isosceles triangle.

Mathematics

A quadrilateral is shown. One pair of opposite sides have lengths of 10 inches and (x + 2) inches. The other pair of opposite sides have lengths (x + 5) inches and (2 x minus 3) inches. Based on the measures shown, could the figure be a parallelogram? 1.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in. 2.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. 3.No, there are three different values for x when each expression is set equal to 10. 4.No, the value of x

Step-by-step answer

P Answered by Master

Sides given by

10x+2x+52x+3

Opposite sides must be equal

Let's check once

$\\ \tt\hookrightarrow x+5=2x+3\implies x=2$

Find sides now

10in2+2=4in2+5=7in2(2)+3=4+3=7in

One pair of opposite sides are equal but others not .

It's a trapezium.

Mathematics

Match the vocabulary word with the correct definition.1. trapezoid a trapezoid with legs of the same length. 2. bases of a trapezoid a quadrilateral with at least one pair of parallel sides. 3. legs of a trapezoid the parallel sides. 4. median of a trapezoid the segment connecting the midpoints of the legs. 5. isosceles trapezoid the nonparallel sides

Step-by-step answer

P Answered by PhD

2

Trapezoid:

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.

Bases of a trapezoid:

The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.

Legs of a trapezoid:

The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.

Median of a trapezoid:

The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.

Isosceles trapezoid:

As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.

Therefore, the right matches are

1. Trapezoid: A quadrilateral with at least one pair of parallel sides.

2. Bases of a trapezoid: The parallel sides.

3. Legs of a trapezoid: The nonparallel sides.

4. Median of a trapezoid: The segment connecting the midpoints of the legs.

5. Isosceles trapezoid: A trapezoid with legs of the same length.

Mathematics

Need . just need my answers checked. in advance. my answers are in brackets. 1. the coordinates of the vertices of δjkl are j(-5, -1) , k(0, 1) , and l(2, -5). which statement correctly describes whether δjkl is a right triangle? a. δjkl is a right triangle because jk is perpendicular to jl. b. δjkl is a right triangle because jl is perpendicular to kl. c. δjkl is a right triangle because jk is perpendicular to kl. [ d. δjkl is not a right triangle because no two of its sides are perpendicular. ] 2. the coordinates of the vertices of δjkl are j(0,

Step-by-step answer

P Answered by Specialist

6

#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

#1) The slope of any line segment is found using the formula

$m=\frac{y_2-y_1}{x_2-x_1}$

For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0. For KL this gives us (1--5)/(0-2) = 6/-2 = -3. For LJ this gives us (-5-1)/(2--5) = -6/7. None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.

#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3. The slope of KL is (1--5)/(3-1) = 6/2 = 3. The slope of LJ is (2--5)/(0-1) = 7/-1 = -7. Two of these slopes have a product of -1, 3 and -1/3. This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.

#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4. The slope of EF is (4-0)/(2-0) = 4/2 = 2. The slope of FG is (0-1)/(0--4) = -1/4. The slope of GD is (1-5)/(-4--2) = -4/-2 = 2. Opposite sides have the same slope so they are parallel.

Next we use the distance formula to find the length of each side:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Using our points, the length of DE is

$\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}$

The length of EF is

$d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}$

The length of FG is

$d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}$

The length of GD is

$d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}$

Opposite sides have the same length and are parallel, so this is a parallelogram.

#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1. The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6. The slope of CD is (1--3)/(5-1) = 4/4 = 1. The slope of DA is (-3--1)/(1--4) = -2/5. Only one pair of opposite sides is parallel, so this is not a parallelogram.

#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7. The slope of QR is (4-0)/(3-5) = 4/-2 = -2. The slope of RS is (0--2)/(5--3) = 2/8 = 1/4. The slope of SP is (-2-2)/(-3--4) = -4/1 = -4. Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.

Mathematics

Need . just need my answers checked. in advance. my answers are in brackets. 1. the coordinates of the vertices of δjkl are j(-5, -1) , k(0, 1) , and l(2, -5). which statement correctly describes whether δjkl is a right triangle? a. δjkl is a right triangle because jk is perpendicular to jl. b. δjkl is a right triangle because jl is perpendicular to kl. c. δjkl is a right triangle because jk is perpendicular to kl. [ d. δjkl is not a right triangle because no two of its sides are perpendicular. ] 2. the coordinates of the vertices of δjkl are j(0,

Step-by-step answer

P Answered by Specialist

6

#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

#1) The slope of any line segment is found using the formula

$m=\frac{y_2-y_1}{x_2-x_1}$

For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0. For KL this gives us (1--5)/(0-2) = 6/-2 = -3. For LJ this gives us (-5-1)/(2--5) = -6/7. None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.

#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3. The slope of KL is (1--5)/(3-1) = 6/2 = 3. The slope of LJ is (2--5)/(0-1) = 7/-1 = -7. Two of these slopes have a product of -1, 3 and -1/3. This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.

#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4. The slope of EF is (4-0)/(2-0) = 4/2 = 2. The slope of FG is (0-1)/(0--4) = -1/4. The slope of GD is (1-5)/(-4--2) = -4/-2 = 2. Opposite sides have the same slope so they are parallel.

Next we use the distance formula to find the length of each side:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Using our points, the length of DE is

$\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}$

The length of EF is

$d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}$

The length of FG is

$d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}$

The length of GD is

$d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}$

Opposite sides have the same length and are parallel, so this is a parallelogram.

#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1. The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6. The slope of CD is (1--3)/(5-1) = 4/4 = 1. The slope of DA is (-3--1)/(1--4) = -2/5. Only one pair of opposite sides is parallel, so this is not a parallelogram.

#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7. The slope of QR is (4-0)/(3-5) = 4/-2 = -2. The slope of RS is (0--2)/(5--3) = 2/8 = 1/4. The slope of SP is (-2-2)/(-3--4) = -4/1 = -4. Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.

Mathematics

Just two multiple choice. 1. the coordinates of triangle xyz are x(-5, 5), y(-3, 2), and z(4, 0). which statement correctly describes whether triangle xyz is a right triangle? a. triangle xyz is a right triangle because xy is perpendicular to xz. b. triangle xyz is a right triangle because xy is perpendicular to yz. c. triangle xyz is a right triangle because xz is perpendicular to yz. d. triangle xyz is not a right triangle because no two sides are perpendicular. 2. the coordinates of the vertices of a quadrilateral defg are d(-2, 5), e(2, 4),

Step-by-step answer

P Answered by Specialist

5

Below are the answers:

1. d. Triangle XYZ is not a right triangle because no two sides are perpendicular.

2. a. Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.

Mathematics

Complete the proof to show that abcd is a parallelogram. on a coordinate plane, quadrilateral a b c d is shown. point a is at (negative 2, negative 2), point b is at (negative 3, 4), point c is at (2, 2), and point d is at (3, negative 4). the slope of line segment b c is startfraction 4 minus 2 over negative 3 minus 2 endfraction = negative two-fifths the slope of line segment a d is startfraction negative 4 minus (negative 2) over 3 minus (negative 2) endfraction = startfraction negative 4 + 2 over 3 + 2 endfraction = negative two-fifths the

Step-by-step answer

P Answered by PhD

31

The answer is slopes of opposite sides are equal

Step-by-step explanation:

Mathematics

Just two multiple choice. 1. the coordinates of triangle xyz are x(-5, 5), y(-3, 2), and z(4, 0). which statement correctly describes whether triangle xyz is a right triangle? a. triangle xyz is a right triangle because xy is perpendicular to xz. b. triangle xyz is a right triangle because xy is perpendicular to yz. c. triangle xyz is a right triangle because xz is perpendicular to yz. d. triangle xyz is not a right triangle because no two sides are perpendicular. 2. the coordinates of the vertices of a quadrilateral defg are d(-2, 5), e(2, 4),

Step-by-step answer

P Answered by Master

5

Below are the answers:

1. d. Triangle XYZ is not a right triangle because no two sides are perpendicular.

2. a. Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.

Mathematics

If we wanted to prove quadrilateral MNOP was a parallelogram, which method below would not work? 1.Doing four slope formulas to show both pairs of opposite sides are parallel. 2.Doing two midpoint formulas to show the diagonals intersect at the same point. 3.Doing two slope formulas and two distance formulas to prove the same pair of opposite sides is congruent and parallel. 4.Doing two distance formulas to show that adjacent sides are not the same length

Step-by-step answer

P Answered by PhD

The correct option is 4.

4) Doing two distance formulas to show that adjacent sides are not the same length.

Step-by-step explanation:

Parallelogram is a quadrilateral which has opposite sides equals and parallel. Example of a parallelogram are rhombus, rectangle, square etc.

We can prove that a quadrilateral MNOP is a parallelogram. If we find the slopes of all four sides and compare those of the opposite ends, same slopes would indicate the opposite sides are parallel, hence the quarilateral is a parallelogram. We can also find the distance of two opposing sides, and slopes of twp opposing sides to determine whether it is a parallelogram or not. The most difficult approach is that diagonals bisect each other at same point.

However, using only two distance formulas will not give us enough information to determine whether a side is parallel or not.

A quadrilateral has one pair of parallel sides with lengths 1 3/4 inches and 1 1/4 inches, and two angles that each measure 36°.

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