Mathematics College

in the given figure ,o is the centr of the circle, ab is the diameter and do is perpendicular to ab. prove that angle AEC= ANGLE ODA​

In The Given Figure ,o Is The Centr Of The Circle, Ab Is The Diameter And Do Is Perpendicular To Ab.

Answers

Answer 1

The given triangles ΔDOA and ΔABC are right triangles that have a

common vertex at point A.

ΔDOA is similar to ΔABC, and ∠AEC is equal to ∠ABC, therefore, ∠AEC = ∠ODA

Reasons:

The given parameters are;

The diameter of the circle with center O = AB

DO ⊥ AB (DO is perpendicular to AB)

Required:

Prove that ∠AEC = ∠ODA

A two column proof is presented as follows;

Statement [tex]{}[/tex]                                                 Reason

1. AB is the diameter of circle     [tex]{}[/tex]                 1. Given

2. DO is perpendicular to AB [tex]{}[/tex]                     2. Given

3. ∠DOA = 90° [tex]{}[/tex]                                             3. Definition of DO ⊥ AB

4. ∠BCA = 90°   [tex]{}[/tex]                                             4. Thales theorem

5. ∠BCA ≅ ∠BCA [tex]{}[/tex]                                         5. Reflexive property

6. ΔDOA ~ ΔABC   [tex]{}[/tex]                                        6. AA similarity postulate

7. ∠ABC ≅ ∠ODA   [tex]{}[/tex]                                       7. CASTC

8. ∠ABC = ∠ODA   [tex]{}[/tex]                                        8. Definition of congruency

9. ∠AEC ≅ ∠ABC   [tex]{}[/tex]                                        9. Angles in the same segment

10. ∠AEC = ∠ABC   [tex]{}[/tex]                                       10. Definition of congruency

11. ∠AEC = ∠ODA   [tex]{}[/tex]                                        11. Transitive property of equality

In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity

postulate, therefore, the three angles of ΔDOA are congruent to the three

angles of ΔABC.

Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles

are Congruent, CASTC.

Learn more about circle theorem here:

https://brainly.com/question/16879446

Related Questions

Please help me solve this math problem

Answers

Answer:

 (b)

Step-by-step explanation:

A suitable calculator or spreadsheet can find the matrix product for you. Here, the answer choices differ in their upper left term, so we can determine the correct choice by finding the value of that term. It is the dot product of the first row of B and the first column of A.

  (5)(3) +(7)(3) +(3)(2) = 15 +21 +6 = 42

This matches choice B.

which holds the more capacity 0.75 litres or 350ml

Answers

Answer:

0.75 liters

Step-by-step explanation:

1000ml in 1 liter so 0.75*1000=750ml

750ml > 350ml

Please help ASAP!!! Will give 10 pts!!​

Answers

A. Mixed
B. Proper
C. Mixed
D. Proper
E. Improper
F. Improper
G. Improper
H. Mixed
I. Improper
J. Improper
K. Mixed
L. Mixed
M. Proper
N. Proper
O. Mixed

Sue has 100 dimes and quarters. If the total value of the coins is &21.40, how many of each kind of coin does she have?

Answers

Answer:

Let x be the number of dimes and y the number of quarters

x +y = 100

a dime is $0.10 and a quarter is $0.25

0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals

10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.

10x + 25(100 -x) = 2140

10x + 2500 - 25x =2140

2500 - 15x = 2140

360 = 15x x = 24 and y = 76

There are 24 dimes and 76 quarters

Answer:

76 Quarters = $19.00

24 Dimes = $2.40

$19.00 + $2.40 = $21.40

Step-by-step explanation:

Yaga

need help solving this

Answers

Answer:

x ≈ 41.6°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{JK}{KL}[/tex] = [tex]\frac{80}{90}[/tex] = [tex]\frac{8}{9}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{9}[/tex] ) ≈ 41.6° ( to the nearest tenth )

GEOMETRY MULTIPLE CHOICE

Answers

Answer:

E seems to be the only one that is true

Step-by-step explanation:

its just asking you basically which ones are true based on the info they already give you

I do believe the Answer is E

PLEASE HELP ILL GIVE BRAINLIESTTTT

Answers

Answer:

f(-4a) = -16a + 8

Step-by-step explanation:

Substitute -4a into the equation

4x(-4a) + 8 = -16a +8

First guy is right!!

Find the perimeter of the figure. Use 3.14 for 7 and round to at least 1 decimal place.

Answers

Answer:

the perimeter of the figure is 27.4 mi

Step-by-step explanation:

rectangle perimeter = 6+6+6 = 18

half circle perimeter = 1/2 2πr = 3.14 × 3 = 9.42

the perimeter of the figure is 18+9.42 = 27.42 --> 27.4 mi

A shipping container will be used to transport several 60-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 26000 kilograms. Other shipments weighing 13200 kilograms have already been loaded into the container. What is the greatest number of 60-kilogram crates that can be loaded into the shipping container?

Answers

Answer:

213 crates

Step-by-step explanation:

There is enough space for 26000 kg - 13200 kg = 12800 kg. Divide this by 60 and you get 213 and 1/3. You cannot put 1/3 of a crate, so it is 213 crates.

Helpppppppp me …………………..

Answers

Answer:

first let's solve for x

x + (x + 30) + 2x = 180

4x + 30 = 180

-30          -30

4x = 150

/4      /4

x = 37.5

Now solve for the angle measures:

(x + 30)    =    (37.5 + 30) = 67.5

2x       =        2(37.5) = 75

x = 37.5

Answer:

X= 37.5

Step-by-step explanation:

My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.

Answers

By knowing that S is bisected by the line shown, we will conclude that PD = 8

So here we know that PC = 8, we also can see that:

PCS is a right trianglePDS is a right triangle.

Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.

Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.

And notice that both of these triangles share one side, then:

Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.

This implies that the triangles are congruent, thus, the measures of the corresponding sides must be the same.

Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.

So you are correct.

If you want to learn more about congruent triangles, you can read:

https://brainly.com/question/12077512

Antonio wants to examine the sales in a restaurant during a period of time from 2 hours before to 2 hours after the peak dinner time and graph his results. If the peak dinner time is considered to be at 6 p.m., what would be the domain for the graph Antonio is creating?

Answers

Using function concepts, it is found that the domain of the graph Antonio is creating would be: [tex]4 \leq x \leq 8[/tex]

The domain of a function is the set that contains all possible input values.

In this problem, the inputs are the time, between 2 hours before and 2 hours after the peak time of 6 pm, hence, it is given by: [tex]4 \leq x \leq 8[/tex]

For more on the domain of functions, you can check https://brainly.com/question/24374080

PLEASE HELP IM BEING TIMED!
Ivan is making cookies for a party. He has 5 cups of flour. The recipe calls for 2 cups of flour. Ivan wants to double the recipe.
Which statement about the amount of flour for the doubled recipe is true?
O A. Ivan has 1 cups of flour more than he needs.
B. Ivan has
5
cup of flour more than he needs.
O c Ivan has exactly enough flour.
D. Ivan needs
cup more flour than he has.
OE. Ivan needs 1
cups more flour than he has.

Answers

The answer is He needs 1/3 more cups of flour than he has.

(2 2/3) x 2 = 16/3 = 5 1/3

The recipe calls for 2 cups of flour. The double of this amount is :

[tex]\mathfrak{2*2} [/tex]

[tex]\underline{\mathfrak{=4}} [/tex]

If Ivan has 5 cups, then :

[tex]\mathfrak{5-4} [/tex]

[tex]\underline{\mathfrak{=1}} [/tex]

So, O A. Ivan has 1 cup of flour more than he needs.

[tex]\mathbb{MIREU} [/tex]

HELPPP!! DUE NOWWWW!

Lucy recently joined a fitness club, she had to pay an initial fee to join. Lucy will also pay an extra fee per class she takes there. The equation below represents the relationship.


f(x)=20+3x


Identify the false statement


A. Lucy paid $3 per class.

B. f(x) represents the total amount Lucy paid.

C. x represents the cost of classes.

D. The initial fee was $20

Answers

Answer: C

Step-by-step explanation: x represents the number of classes, not the cost of classes.

Solve for X
5x-8 Answer is not 4.5 or 9/2

Answers

Answer:

[tex]{ \rm{5x - 8 < x + 10}} \\ \\ { \rm{5x - x < 10 + 8}} \\ \\ { \rm{4x < 18}} \\ \\ { \rm{x < 4.5}}[/tex]

Solving for x in the inequality gives us;

x < 4.5

Inequality

We are given the inequality;

5x - 8 < x + 10

The first step is to use addition property of equality to add 8 to both sides;

5x - 8 + 8 < x + 10 + 8

5x < x + 18

Use subtraction property of equality to subtract x from both sides to get;

5x - x < x + 18 - x

4x < 18

Using division property of equality, we have;

x < 18/4

x < 4.5

Read more on inequalities at; https://brainly.com/question/25275758

The length of a rectangular garden is 3 feet more than 2 times the width. The perimeter of the garden is 48 feet. Find the length and width of the garden .

Answers

Answer:

  length 17 feet

  width 7 feet

Step-by-step explanation:

Let w represent the width. Then the length is 2w+3, and the perimeter is ...

  P = 2(L +W)

  48 = 2((2w+3) +w) = 6w +6

  42 = 6w

  7 = w . . . . . . . . width

  (2w+3) = 17 . . . length

The length of the garden is 17 feet; its width is 7 feet.

Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone

Answers

Answer:

5 weeks

Step-by-step explanation:

The amount of money he has to earn in order to buy the phone is: 400-55 = 345( dollars)

He gets 345 dollars in: 345÷75= 4 weeks and remains 45 dollars

So he needs to work for 1 more week to have enough money to buy the phone

So he needs to work at least 5 weeks

which statement is true

Answers

Morgan earns more money per hour on Friday

Mary has some chocolates. If she shares them equally among 4 friends or 5 friends, there are always 2 extra chocolates left. What is the possible number of chocolates Mary could have?

Answers

Answer:

22 chocolates

Step-by-step explanation:

First, let x represent the number of chocolates Mary has. Since she always has 2 extra chocolates, the number of chocolates distributed to her friends would be x - 2. And x - 2 is the least common multiple of 4 and 5 because x - 2 chocolates are evenly distributed among 4 and 5 friends. The LCM of 4 and 5 is 20, so x - 2 is 20.  Mary has 22 chocolates.

Select the correct answer from each drop-down menu.
what is 1 plus 1

Answers

one plus one equals 2 let me know if you need more help

The diagram shows the distance between my home, H. and two towns, A and B.

It also shows information about journey times.

What is the average speed of the journey from my home to town A?

Answers

I do not know English :33333

heeeeeeeeeeeeeeeeeeeelp me plssssssssssss

Answers

Answer:

Yep linear functions look like diagonal lines. Vertical lines have a slope of 0 whilst horizontal lines aren’t even defined. Diagonal and horizontal don’t work since horizontal aren’t defined so if one doesn’t work then it won’t work.

So (a) is the answer

Diagonal lines are linear functions

Answer:

Diagonal lines........


give a pair of alternate interior angles, a pair of corresponding angles and a pair of alternate exterior angles.

Answers

alternate interior: 6&3
corresponding: 5&7
alternate exterior: 8&1

Help me please I don’t know what to don

Answers

The mistake was in the distributive property
4y-(5-9y) =4y-5-9y

It should’ve been 4y-5+9y

write an expression to represent admission to a zoo of $10.00 and the cost of special exhibits s at $4 each. Evaluate you expression when s=2

Answers

Answer:

10.00 +4s .

u wanted expression ,  not answer.?

Step-by-step explanation:

Draw two lines with a slope of 1 / 2. What do you notice about the lines?

Answers

Answer:

The lines would be parallel.

Step-by-step explanation:

lines with the same slope are parallel.

The lines 1/2 should be parallel lines :)

If xy + xb + ya + ab = 32 and x + a = 4 , then x + b = ​
and i will give BRAINLIEST

Answers

Answer:

Step-by-step explanation:

If you're actually looking for y + b rather than x + b

Then

xy + xb + ya + ab = (x + a)(y + b) = 32

                                        4(y + b) = 32

                                           y + b = 8

otherwise we have a situation with only two equations and four unknowns. This cannot be resolved without further information.

pls help me anymore pls​

Answers

Answer:

thanks for the points again

Step-by-step explanation:

,(TT(TT)(TT)(TT)(TT)(TT)(TT

you walk 3/4 miles to a grocery store. Then you walk another 1/5 miles to a shoe store. How many miles have you walked in all?

Answers

Answer:

19/20 miles

Step-by-step explanation:

3/4 + 1/5

3/4 = 0.75

1/5 = 0.2

3/4 + 1/5

= 0.75 + 0.2

= 0.95

= 95/100

= 19/20

Therefore,

the miles you have walked in all is 19/20.

Helpppo for an exammmm

Answers

Answer:

AAS

Step-by-step explanation:

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