All categories

3 years ago

Determine if KLMN must be a parallelogram. Justify your answer.

Mathematics

2 answers:

Ludmilka [50]3 years ago

7 0

Answer:

(D)

Step-by-step explanation:

For there too be a parallelogram, you must have two pairs of opposite side parallel lines. This means that KN & LN must be parallel, and KL & NM have to be parallel.

vovikov84 [41]3 years ago

4 0

Answer:

Choice C

One pair of opposite sides are parallel (KN and LM). That same pair of opposite sides are also congruent. Therefore, the figure is a parallelogram.

==============================================

The tick marks tell us that the sides are congruent. So KN = LM. In short, they are the same length.

They are also parallel because of the similar arrow markers that are in the middle of the segment. If the arrows were at the endpoint of the segment, then you would have a ray. But being in the middle of the segment means "this line is parallel to any other line with the same arrow marker in the same basic position".

With this set of info, we can draw in line KM and show that angle NKM = angle LMK (alternate interior angles). Then by SAS, we can show that triangle NKM = triangle LMK. Finally, using CPCTC, we can show that KL = NM and that angle KMN = angle MKL

The fact that angles KMN and MKL are alternate interior angles would help us prove that KL and MN are parallel.

So in short, we have enough info to prove the figure is a parallelogram. Even though at first glance, it may seem that this figure is not a parallelogram (since only one pair of opposite sides are parallel).

You might be interested in

a 10-foot section of a certain rope weighs 8 ounces. What is the length, in feet, of a section that weights 3 pounds? can you pl

Ostrovityanka [42]

Create and solve an equation of ratios:

10 ft 8 oz
------- = -------
x 48 oz (note that 3 lb = 48 oz)

Then 480 = 8x, and x = 60 ft (answer)

6 0

3 years ago

Heidikae reads 420 pages a week. In the summer, she reads 17% less. Approximately how many pages per week does she read in the s

Marat540 [252]

420-17%= 348.6

This is it because she read 420 pages during the summer but then she reads 17% less which is subtracting then get the answer which is 348.6

8 0

3 years ago

The Quick Change Oil Company has a number of outlets in the metropolitan Seattle area. The daily number of oil changes at the Oa

Rashid [163]

Answer:

5 classes.

Step-by-step explanation:

You can use the $2^k$ rule to determine the number of classes for a frequency distribution.

The $2^k$ rule says that $2^k\geq n$ where

$k$ is the number of classes

$n$ is the number of the data points

We know that the number of data points is $n$ = 20.

Next, we start searching for $k$ so that we can get a number 2 to the $k$ that is larger that the number of data points.

$2^4=16\\2^5=32$

This suggests that you should use 5 classes.

8 0

3 years ago

What is the security for the payment of a secured loan called

igomit [66]

The answer is C) collateral

8 0

3 years ago

Miguel is mixing up a salad dressing. regardless of the number of servings, the recipe requires that 5/8 of the finished dressin

olga_2 [115]

The remainder is 1-5/8-1/4=8/8-5/8-2/8=1/8.
If the quantity of dressing was 24oz, then there would be 15oz of olive oil, 6oz of vinegar and 3oz of mixture, consisting of 1oz each of salt, pepper and sugar.
If the vinegar doubles we have 12oz of vinegar. The quantity of ingredients is 15oz of olive oil, 12oz of vinegar, and 2oz of mixture (no sugar) making 29oz altogether. The proportion of olive oil is therefore 15/29.

7 0

3 years ago