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
Burka [1]
3 years ago
7

Given: △ABC, AB = CB AK ⊥ BC , MC ⊥ AB Prove: AK = MC

Mathematics
1 answer:
MatroZZZ [7]3 years ago
5 0

By using congruence of two triangles AKC and CMA we proved that

AK = MC

Step-by-step explanation:

Lets revise the cases of congruence  

  • SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
  • SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and   including angle in the 2nd Δ
  • ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  ≅ 2 angles and the side whose joining them in the 2nd Δ
  • AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles   and one side in the 2nd Δ
  • HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ

In Δ ABC

∵ AB = BC

∴ Δ ABC is an isosceles triangle

∴ ∠BAC ≅ m∠BCA ⇒ base angles of isoscelesΔ

∵ AK ⊥ BC

∴ m∠AKC = 90°

∵ MC ⊥ AB

∴ m∠CMA = 90°

∴ ∠AKC ≅ ∠CMA

In the two Δs AKC and CMA

∵ ∠BAC ≅ m∠BCA

∵ ∠AKC ≅ ∠CMA

∵ AC ≅ CA

∴ Δ AKC and Δ CMA are congruent by AAS postulate

∴ AK ≅ CM

By using congruence of two triangles AKC and CMA we proved that

AK = MC

Learn more:

You can learn more about congruence in brainly.com/question/3202836

#LearnwithBrainly

You might be interested in
10 Points<br> Can someone explain to me how to solve this
tatyana61 [14]

Answer:

d he didn't make a mistake

Step-by-step explanation:

so when is says comparing to one it means is the fraction greater than less than or equal to one and because 3/4 is less than one and 9/8 is greater than then 3/4 is less than 9/8 remember it always opens up to the larger number

8 0
3 years ago
Work out the size of angle EAB. <br> You must give a reason for each stage of your working.
Nadya [2.5K]
There’s no photo so we can’t help you sorry :(
7 0
2 years ago
Model subtraction of fraction:
cricket20 [7]
The entire race is 1 full race.
One full race is 1.
He ran 3/8 of 1, so he ran 3/8.
He needs to run the rest of the race.
The rest is unknown, so we call it x.
When you add 3/8 to the unknown, you get the full race.
The equation is

x + 3/8 = 1

Change 1 to a denominator of 8.

x + 3/8 = 8/8

Subtract 3/8 from both sides.

x = 5/8

Answer: He still needs to run 5/8 of the race.
5 0
3 years ago
Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the
vladimir2022 [97]

The number of tiles used is 300 tiles.

According to the statement

We have given that:

The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.

And we have to find that the number of tiles used to prepare the dark room.

So, For this purpose we have to find the area of the room floor.

The area of the floor is 6 *3.

The area of the floor is 18 meter per square.

The area of the tile is 0.2*0.3

The area of the tile is 0.06 meter per square.

Now,

The number of tiles used is 18/0.06

The number of tiles used is 300.

So, The number of tiles used is 300 tiles.

Learn more about Area here brainly.com/question/10090807

#SPJ1

7 0
2 years ago
A particular battery claims to have a mean life of 400 hours with a standard deviation of 30 hours. Approximately what percent o
Svetach [21]

Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, we have that the mean and the standard deviation are given, respectively, by:

\mu = 400, \sigma = 30.

The proportion of the batteries will last more than 420 hours is <u>one subtracted by the p-value of Z when X = 420</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{420 - 400}{30}

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514.

0.2514 = 25.14% of the batteries will last more than 420 hours.

More can be learned about the normal distribution at brainly.com/question/24663213

#SPJ1

3 0
2 years ago
Other questions:
  • (4n+4)(5n-8)
    6·1 answer
  • Please answer this correctly
    6·1 answer
  • What is the slope of the line shown below? (4, 8) (2, 4)
    6·2 answers
  • Guys I need help.....
    9·2 answers
  • a pet store sells tropical fish one week they sell 18 angelfish, 6 tetras,and 39 guppies . the owner uses ratios of sales to com
    8·1 answer
  • What is 130/400 in simplest form as a decimal
    11·2 answers
  • Solving systems of equations by substitution<br> y= x - 8<br> y = -4
    13·1 answer
  • Write the additive and multiplicative inverse of -1/2​
    11·2 answers
  • Write an equation in Slope-Intercept Form using the table below. ​
    14·1 answer
  • Suppose V is the midpoint of UW, and TV = XV. What additional information would you need to conclude that TUV = XWV using the SA
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!