All categories

3 years ago

Prove that kn=mp and knmp is a parallelogram

Mathematics

1 answer:

____ [38]3 years ago

3 0

Answer:

See the paragraph proof below.

Step-by-step explanation:

Quadrilateral JKLM is given as a parallelogram. By a theorem, opposite sides JK and LM are congruent (1). By the definition of parallelogram, opposite sides KJ and ML are parallel. By the theorem on alternate interior angles, angles KJL and MLJ are congruent (2). Segments JN and PL are given as congruent (3). Using the three statements of congruence labeled above (1), (2), and (3), we now prove that triangles JKN and LMP are congruent by SAS. Sides of the triangles KN and PM are congruent by CPCTC. Sides of quadrilateral KNMP are given as parallel. Therefore, quadrilateral KNMP is a parallelogram by the theorem: If two sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

You might be interested in

Matching quantities with units

Mrrafil [7]

Answer:

1. Volume = length x width x height => cubic centimetres.

2. Perimeter = 2(length) + 2(width) => metres.

3. Speed = Distance /time => metres per second.

4. Area = length x width => square metres.

Step-by-step explanation:

1. Volume = length x width x height

If the length, width and height are measured in centimetre (cm) , then, the unit of the volume will be:

Volume = cm x cm xcm = cm3 i.e cubic centimetres.

2. Perimeter = 2(length) + 2(width)

If the length and width are measured in meter (m), then, the unit of the perimeter will also be in metre (m).

3. Speed = Distance /time

If the unit of distance is measured in metre (m) and the time is measured in second (s), then , the unit of the speed will be:

Speed = Distance /time = m/s i.e metres per second.

4. Area = length x width

If the length and width are measured in metres (m), then, the unit of the area will be:

Area = m x m = m2 i.e square metres

8 0

3 years ago

The quantity of soap produced in 2009 is 3000bars. if this is a 20% increase of what was produced in 2008.what is the quantity o

mr Goodwill [35]

2,400
20% of 3,000= 600
3,000 - 600= 2,400

6 0

3 years ago

Dilate by a scale<br> factor of 1/2<br> AL<br> D

Firdavs [7]

Answer:

The image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

D' (0, 1)

L' (1/2, 5/2) or L'(0.5, 2.5)

W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

Step-by-step explanation:

Given the triangle ΔDLW withe the vertices

D(0, 2)

L(1, 5)

W(5, 4)

As the scale factor 1/2 < 0, thus the image triangle will be smaller than the original triangle.

The rule of dilation is given by

Dilation: (x, y) → (1/2x, 1/2y), centered at (0, 0)

D(0, 2) → D' (1/2x, 1/2y) → D' (1/2(0), 1/2(2)) = D' (0, 1)

L(1, 5) → L'(1/2x, 1/2y) → L'(1/2(1), 1/2(5)) = L' (1/2, 5/2)

W(5, 4) → W'(1/2x, 1/2y) → W'(1/2(5), 1/2(4)) = W' (5/2, 2)

Therefore, the image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

D' (0, 1)

L' (1/2, 5/2) or L'(0.5, 2.5)

W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

7 0

3 years ago

The sum of Jada and Sophie's ages is, at most, 18. Sophie is 3 years older than twice Jada's age. Write an inequality model Jada

liq [111]

Answer:

Step-by-step explanation:

$s=2j+3\\ \\ j+s\le 18\\ \\ j+2j+3\le 18\\ \\ 3j+3\le 18\\ \\ 3j\le 15\\ \\ j\le 5\\ \\ \text{Though j=5 is the only solution to both equations.}$

5 0

2 years ago

What is .0067 .007 .00618 .00701 .006 arranged in largest to smallest

Sidana [21]

00701, .007, .0067, .00618, .006
Step 1 : Compare the whole numbers.Step 2 : When whole numbers are same check the decimal places.Step 3 : Convert into like decimals considering the maximum decimal number.The correct order is .00701, .007, .0067, .00618, .006

5 0

3 years ago

Prove that kn=mp and knmp is a parallelogram ​

Prove that kn=mp and knmp is a parallelogram