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
s344n2d4d5 [400]
3 years ago
12

Based only on the information given in the diagram, which congruence

Mathematics
1 answer:
romanna [79]3 years ago
8 0
<h3>1 Answer: Choice D) SAS</h3>

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

Explanation:

LA stands for Leg Angle. More specifically, the angle is an acute angle. This theorem only works for right triangles. We see that ED = LK which is one pair of congruent leg segments. So that takes care of the L part of LA. However, we don't know anything about the acute angles. We don't know if angle E = angle L, or if angle F = angle M, or something along those lines. We need angle markers to tell us or not.

In short, we only have half the info needed for LA, so we must cross choice A off the list.

----------------

HA stands for hypotenuse angle, or hypotenuse acute angle, and this rule only applies for right triangles. We don't know anything about the hypotenuse lengths if they are the same or not.

Similar to choice A, we don't know anything about the acute angles either.

Those two facts mean we must cross off choice B.

----------------

AAS stands for Angle Angle Side. The order is important because the side is not between the angles. The diagram only shows one pair of angles that are congruent to one another. That pair being the 90 degree angles indicated with the square marker. We don't have another pair of angles, so we cannot use AAS.

Cross choice C off the list.

-----------------

We can use SAS because we have two pairs of congruent sides and one pair of congruent angles.

The congruent sides are

  • ED = LK (double tickmarks)
  • DF = KM (single tickmarks)

That takes care of the two "S"s of "SAS". The "A" would be those two right angles which are congruent to one another. The angles are between the congruent sides which is important. Recall that SSA is not a valid congruence theorem.

So that's why choice D is the only answer.

-----------------

Side note: We could use the LL theorem, where L stands for leg, since we are given two pairs of congruent legs for each triangle. Like LA and HA, this only applies to right triangles. LL is a special case of SAS. However, LL isn't listed so we'll just be sticking with SAS as the only answer.

You might be interested in
Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.
KatRina [158]

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30      Eqn 1

x+6y=11.25      Eqn 2

Multplying Eqn 2 by 2

2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 1

(4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50

Dividing both sides by 2

\frac{2x}{2}=\frac{7.50}{2}\\x=3.75

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11821063
  • brainly.com/question/11871074

#LearnwithBrainly

3 0
3 years ago
Evaluate the trigonometric funtion of the angle theta​
jeka57 [31]
The last side would be 10
8 0
2 years ago
5. photo album: $25.50, 10% markup
sasho [114]

Answer:

$28.05

Step-by-step explanation:

If you want to find how much the photo album is after the markup, you first have to find 10% of the original price. 10% of $25.50 is $2.55, so you add $2.55 and $25.50 to find the price after the markup.

Hope this helps!

3 0
3 years ago
What is the absolute value of |4.7|
larisa86 [58]

Answer:

4.7

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find the pattern and the next number<br> 6, 13, 26, ___??
AnnZ [28]

Answer:

53

Step-by-step explanation:

By examining the numbers and evaluating how the pattern changes, you should have 53 as the upcoming number after 26.

So,

6, 13, 26, <u>53</u>

3 0
3 years ago
Other questions:
  • A house has increased in value by 38% since it was purchased. If the current value is $621,000 what was the value when it was pu
    13·1 answer
  • Evaluate the function for x = –2a, if a = 3.<br> f(x)= -4x+7
    9·1 answer
  • Questions 2-7 will all be in regards to this data set:Observation X Y1 20 302 23 353 28 404 26 385 24 376 32 457 35 508 24 349 3
    12·1 answer
  • Compare A and B in three​ ways, where A=1.84 million is the 2012 daily circulation of newspaper X and B=2.26 million is the 2012
    10·2 answers
  • How to find distance of a vertical line on the cordinate plane
    14·1 answer
  • jana bowled 5 games .write and solve an equation to find how many points she averaged each game chart says scored 522
    14·2 answers
  • Which of these is an example of a literal equation?
    9·1 answer
  • Who ever gets it right gets a Brainliest
    11·1 answer
  • Quadrilateral MNPQ has vertices M(0,6), N(4,4), P(6. – 1), and Q(2,0). Determine the coordinates of the vertices of the image of
    10·1 answer
  • When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to th
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!