All categories

2 years ago

If JK and LM are congruent and parallel, then JKL and MLK are congruent.

Mathematics

1 answer:

viktelen [127]2 years ago

3 0

Answer:

Given statement is TRUE.

Step-by-step explanation:

Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.

We know that corresponding angles formed by transversal line are congruent.

Hence ∠JKL = ∠ MLK ...(i)

Now consider triangles JKL and MLK

JK = LM {Given}

∠JKL = ∠ MLK { Using (i) }

KL = KL {common sides}

Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.

Hence given statement is TRUE.

You might be interested in

The diagram shows a 3 cm x 5 cm x 4 cm cuboid

Rainbow [258]

Answer:

a) The length of segment AC is approximately 5.83 centimeters.

b) The angle ACD is approximately 34.5º.

Step-by-step explanation:

a) Since $AB \perp BC$ , the length of segment $AC$ is determined by Pythagorean Theorem, that is:

$AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}$

$AC \approx 5.831\,cm$

The length of segment AC is approximately 5.831 centimeters.

b) Since $AB \perp BC \perp AD$ , the length of segment $AD$ is determined by this Pythagorean identity:

$AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}$

$AD \approx 7.071\,cm$

The angle ACD is determined by the following trigonometric expression:

$\cos C = \frac{AC}{CD}$

$\cos C = \frac{5.831\,cm}{7.071\,cm}$

$\cos C = 0.825$

$C = \cos^{-1} 0.825$

$C \approx 34.448^{\circ}$

The angle ACD is approximately 34.448º.

4 0

2 years ago

What is 25% Of 30% Of 400?

marta [7]

Answer:

25% of 30% of 400 = 30

33% decrease in value

Step-by-step explanation:

You can either get 30% of 400 first then 25% of 400 or you can get the total percentage of 400.

Method 1:

30% of 400 = 0.3 of 400 = 0.3 * 400 = 120

25% of 120 = .25 of 120 = .25 * 120 = 30

Method 2:

30% of 25% = 0.3 * 0.25 = 0.075 = 7.5% of 400

7.5% of 400 = 0.075 of 400 = 0.075 * 400 = 30

5.) To find the percentage of the new price, you can build the equation below.

$\frac{new price}{original price} = \frac{percent}{100}$

$\frac{200,000}{300,000} = \frac{x}{100}$

$20,000,000 = 300,000x$

$x = 66.667$

The percentage decrease in price is then 100% of the original price - 66.667% of the original price = 100% - 66.67% = 33.33% = 33% decrease.

3 0

2 years ago

Caroline has 10 marbles. One half of them are blue. How many marbles are blue?

Viktor [21]

Answer: 5

One half of 10 is 10/2 or 1/2(10)
10/2 = 5
1/2(10) = 5

6 0

2 years ago

Read 2 more answers

Consider the composite function (g (x) ) = StartRoot StartFraction 1 Over x squared minus 3 EndFraction EndRoot. If g(x) = x2 –

balandron [24]

Answer:

answer is c

Step-by-step explanation:

8 0

3 years ago

The cost of cementing 30 m² of floor area is $810. How much will it

Y_Kistochka [10]

Answer:

The answer is 1485 m^2

Step-by-step explanation:

27 per m^2 so 27 times 55 = 1485 m^2

6 0

3 years ago

Read 2 more answers