1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgen [1.6K]
3 years ago
13

S KM ∥ JN? Why or why not?

Mathematics
2 answers:
atroni [7]3 years ago
7 0
This is the concept of linear proportionality, triangle JLN and triangle KLM are similar, this implies that:
KL/KJ=ML/MN
which implies that:
16/10=24/15
therefore we conclude that the answer is :
Yes, because 16/10=24/15
bixtya [17]3 years ago
4 0

Given: We have the given figure through which we can see

LK=16,

KJ=10,

LM=24,

MN=15

To Find: Whether KM || JN and the reasoning behind it.

Solution: Yes, KM || JN because \frac{16}{10}= \frac{24}{15}

Explanation:

For this solution, we use the concept of Similar Triangles.

Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Now, ∠MLK=∠NLJ

To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN

LK:KJ=LM:LN\\\\ \frac{LK}{KJ} =\frac{LM}{LN}\\\\\frac{16}{26}= \frac{24}{39}\\\\

which is true as both sides simplify to \frac{8}{13}

Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Therefore, KM || JN.

To come to the reasoning, notice that

\frac{LK}{LJ} =\frac{LM}{LN}\\\\\frac{LK}{LK+KJ} =\frac{LM}{LM+MN}\\\\\frac{LK+KJ}{LK} =\frac{LM+MN}{LM}\\\\1+\frac{KJ}{LK}=1+ \frac{MN}{LM}\\\\\frac{LK}{KJ} =\frac{LM}{MN}

In other words, \frac{16}{10}= \frac{24}{15}


You might be interested in
Use a paragraph, flow chart, or two-column proof to prove the angle congruency. Given: ∠ CXY ≅ ∠ BXY
Llana [10]

Answer:

See explanation

Step-by-step explanation:

Consider triangles CAX and BAX. In these triangles,

  • \overline{AC}\cong \overline{AB} - given
  • \angle CAX\cong \angle BAX - given
  • \overline{AX}\cong \overline{AX} - reflexive property

By SAS postulate, \triangle CAX\cong \triangle BAX

Congruent triangles have conruent corresponding parts. So,

\overline{CX}\cong \overline{BX}

Consider triangles CXY and BXY. In these triangles,

  • \overline{CX}\cong \overline{BX} - proven
  • \angle CXY\cong \angle BXY - given
  • \overline{XY}\cong \overline{XY} - reflexive property

By SAS postulate, \triangle CXY\cong \triangle BXY

Congruent triangles have conruent corresponding parts. So,

\angle XCY\cong \angle XBY

5 0
3 years ago
Please help me ASAP please
lianna [129]

Answer:

Alright so basically

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
An ant can travel at a constant speed of 980 inches every 5 minutes. How far does the ant travel in 1 minute? The ant travels 19
ycow [4]

Answer:

The ant travels 1,372 inches in 7 minutes.

Step-by-step explanation:

Since 1 minute = 196 inches

1 × 7 = 7

196 × 7 = 1,372

8 0
3 years ago
You roll a six-sided dice numbered 1-6, and eight sided dice numbered 1-8, and a ten sided dice numbered 1-10. What is the proba
bezimeni [28]

Answer:

1/480

Step-by-step explanation:

<h3>for the 6 sided one</h3>

rolling a 5 is 1/6

<h3>for the 8 sided one</h3>

rolling a 5 is 1/8

<h3>for the 10 sided one</h3>

rolling a 5 is 1/10

total probability= 1/6*1/8*1/10

= 1/480

8 0
3 years ago
Help anyone I have like 15 more minuets to finish
Naya [18.7K]
The answer is 45 it's the easiest
5 0
3 years ago
Other questions:
  • Point m is the midpoint of line segment ab, b is at (20,4), m is at (18, -2) and a is at (p,q). what is p+q?
    8·1 answer
  • These box plots show daily low temperatures for a sample of days in two different towns.
    14·2 answers
  • A study of six hundred adults found that the number of hours they spend on social networking sites each week is normally distrib
    5·2 answers
  • What is 5 times 1863636373726
    7·2 answers
  • Find X.<br><br> A) 3<br><br> B) 4<br><br> C) 5<br><br> D)6
    6·2 answers
  • I dont know how to find x​
    8·1 answer
  • What is the area of the rectangle?
    7·1 answer
  • Find the area of the shaded region.
    13·1 answer
  • What is the inverse of the function f(x) = 2x + 1?
    14·1 answer
  • Please put answer as a mixed number! :)<br> 1 and 3/8* 1.5 + 5 and 5/8 ÷ 0.4 =
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!