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.

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Related Questions

You have two right triangles that are similar. The base of the first is 8 and the height is 12.
If the base of the second triangle is 22, what is the height of the second triangle?
A. 33 units
B. 26 units
C. 14.7 units
D. 4.4 units

Answers

Let the height be x

[tex]\\ \sf\longmapsto \dfrac{8}{12}=\dfrac{22}{x}[/tex]

[tex]\\ \sf\longmapsto 12x=22(8)[/tex]

[tex]\\ \sf\longmapsto 12x=176[/tex]

[tex]\\ \sf\longmapsto x=14.7units[/tex]

Step-by-step explanation:

X :

8/12 = 22/x

x • 12 = 22 • 8

12x = 176

x = 14.7units (C.)

Select the correct answer. This table represents the boiling point of water at different altitudes.Which equation represents water's boiling point (y) based on the change in altitude (x)? Altitude (thousands of feet) Boiling Point of Water (Fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9

Answers

Answer:

Step-by-step explanation:

The net income reported on the income statement for the current year was $135,500 depreciation recorded on store equipment for the year amounted to $22,400 balances of the current asset and current libaility accounts at the beginning and end of the year are as follows

A CD is on sale for $10.00. The sales tax rate is 6%. How much will the total cost be for the CD

Answers

Answer:

$10.06

Step-by-step explanation:

Tax rate = 6% , convert into 0.06

10 × 0.06 = 0.6

10 + 0.6 = 10.06

I want a way to solve such a problem​

Answers

Answer:

11.2

Step-by-step explanation:

The rectangular prism shown is formed by six intersecting planes.

Where do the planes ABFE and EFGH intersect

Answers

Answer:

Line EF

Step-by-step explanation:

Planes intersect at lines

The planes ABFE and EFGH intersected by line EF.

What is Prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

We have cuboidal prism which have faces ABFE and EFGH.

To find the point for intersecting we have to find a point or line which is common in both planes.

Here the point E and F are common.

But the plane EF is also common

Thus, the intersecting line is line EF.

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This is Functions and Statistics Class:

Answers

[tex] \sqrt[6]{x} . \sqrt[4]{ {y}^{3} } \\ = {x}^{ \frac{1}{6} } . {y}^{ \frac{3}{4} } \\ = {x}^{ - 6} . {y}^{ \frac{3}{4} } [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

what is an equation of the line that passes through points (-7,-5) and (-7,-2)?

Answers

Answer:

I think I've answered this question already.

Step-by-step explanation:

For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7

Answers

Answer:

x=33

Step-by-step explanation:

you move the 4 to the other side

x=7-4

so

x=3

Answer:

x=3

Step-by-step explanation:

This should be easy.

4+x=7

-4    -4

x=7-4

x=3

Word explanation:

Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.

Sally gets $8.00 each week for allowance. She wants to purchase a used bicycle that costs $24.00. She also wants to donate $8.00 to the food kitchen. Label your drawings with bike.

1. How much money will she have to save for both?

2. How many weeks will it take her to save for both?

3.How many weeks will she have to save if she wants to buy a newer used bicycle
that costs $32.00 and still make her $8.00 donation?

Answers

Answer:

1: $32. 2: 4 weeks. 3: 5 weeks

Step-by-step explanation:

1: 8+24=32$

2: 32/8=4=4 weeks

3: 32+8=$40

    40/8=5=5 weeks

Martina's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has at least 60 liters. What are the possible numbers of minutes
. :
Martina could add water?
Use t for the number of minutes
Write your answer as an incqua ty solved fort

Answers

Answer:

9 minutes

Step-by-step explanation:

60=15+5t

45=5t : subtract 15 from both sides

9=t : divide by 5 for both side

Help help help math math

Answers

Answer: -1 = (-3/3)

Step-by-step explanation

You go from one point to another, i started from 3,1 and went to 3,0. I got down -3 which is my rise and right 3 for the run. Tell me if this is correct

Help help math math math

Answers

the answer is x = 8

thank u

Answer:

-3/7,0

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINLIEST!

Answers

Answer:

Step-by-step explanation:

[tex]12000(1+\frac{.12}{4})^{4*45}=2454040.31463\\=2454040[/tex]

3. Find the area of the trapezoid.
8 ft
4V3
10 ft

Answers

Answer:

[tex]32\sqrt3[/tex]

Step-by-step explanation:

We need first to find the measure of the red horizontal line, call it x. The triangle i filled is a right triangle, so we can apply pythagoras theorem,

[tex]8^2 = x^2+(4\sqrt3)^2 \rightarrow 64=x^2+(16\times3) \\x^2=64-48 \rightarrow x^2=16 \rightarrow x=4[/tex]

(we are talking lengths of segment so we take only the positive root!)

At this point we can find the length of the smaller base of the trapezoid (which is [tex]10-4=6[/tex]) and apply the formula, or split the figure in a rectangle of sides 6 and [tex]4\sqrt3[/tex] and a triangle of sides [tex]4\sqrt3[/tex] and 4.

With the trapezoid formula

[tex]A=\frac12(B+b)h = \frac12(10+6)4\sqrt3 = 32\sqrt3[/tex]

With the sum of figures:

[tex]A= bh+\frac12 xh=6\times4\sqrt3 +\frac12\times4\times4\sqrt3=24\sqrt3+8\sqrt3=32\sqrt3[/tex]

Mandy spins a biased spinner 3 times. The probability that the spinner will land on blue on all 3 spins is 27/512 Calculate the probability that when the spinner is spun 3 times it does not land on blue on any of the spins​

Answers

Answer:

0.158203125

i think

help me plssssssssssssss

Answers

multipley by 2, to get the answer

someone help please i don’t want to fail math

Answers

Answer:

Image below!

Step-by-step explanation:

Plotting [tex]\underline{y=2x+3}[/tex]

Step 1: determine the y-intercept

[tex](0,3)[/tex]

plot the point as the first point on the graph

Step 2: Move 2 units up, and 1 unit left (keep repeating this process until you have reached the limit of the graph)

Step 3: Go to the other side of the graph of the first point (y-intercept)

move 2 units down, and 1 unit right keep repeating this process until you have reached the limit of the graph)

When you've completed this process, it should look like this:

Which inequality matches the graph?

Answers

Answer:

x < 2/3 y + 2 1/3

Step-by-step explanation:

put it in a graphing calculator and they matched, I do not know

A graph, a table and equation are shown below. Please help!

Answers

Answer:

A) slope is 1

B) Slope is 3

C) slope is 0.5

Step-by-step explanation:

Using Rise over run method and mx+b

Recently, your parents read in the newspaper that American factory worker jobs have the lowest income ra
What is the best explanation for this fact?
A A factory worker does not need a lot of education
B Companies are relocating factories to other parts of the world.
C Factories are always in poor areas.
D A computer can do the work a factory worker currently does

Answers

Answer:

A. A factory worker does not need a lot of education.

Step-by-step explanation:

The answer is " A " which is a factory worker does not need a lot of education. since most people don't have a PHD degree or anything higher education, it results in a lot of people joining due to the benefit of the factory worker doesn't need a lot of worker which makes it low in demand too.

solve systems of equations 6x+2y=1 y=-3x+3 using substition??? Need answers quickly!!!!!

Answers

This might be incorrect but I tried my best. My answer is 0.416 but the 6 is repeating

20 charecters lol pls solve

Answers

Answer:

-3x+12

Since we are adding like terms you add everything that has an "x" after it [(3.4x) + (-5.4x) + (-x)] it all that adds up to -3x and the you add the 12 to it. It could also be written 12-3x

Which property explains why these two expressions are equal? 7 + q + 4 = 4 + 7 + q

Answers

Commutative property, the order in adding or multiplying does not matter

Which TWO identify the same sequence?


A) f(x) = 6x + 4 for x = {1, 2, 3, ...}


B) f(x) = 10x + 4 for x = {1, 2, 3, ...}


C) a1 = 6 and an + 1 = an + 4 for n = {1, 2, 3, ...}


D) a1 = 10 and an + 1 = an + 4 for n = {1, 2, 3, ...}


E) a1 = 10 and an + 1 = an + 6 for n = {1, 2, 3, ...}

Answers

A and E are equivalent sequences

The sequences A and E are the same sequences.

What is Sequence?

Sequences are set of numbers where the numbers are arranged in a specific order. Some of the common types of sequences are Arithmetic sequences and Geometric sequences.

A) f(x) = 6x + 4 for x = {1, 2, 3, ....}

f(1) = 10, f(2) = 16, f(3) = 22, ....

B) f(x) = 10x + 4 for x = {1, 2, 3, ...}

f(1) = 14, f(2) = 24, f(3) = 34, ....

C) a₁ = 6 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 6, a₂ = a₁ + 4 = 10, a₃ = a₂ + 4 = 14, ....

D) a₁ = 10 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 4 = 14, a₃ = a₂ + 4 = 18, .....

E) a₁ = 10 and aₙ₊₁ = aₙ + 6 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 6 = 16, a₃ = a₂ + 1 = 22, ....

A and E are the same sequences with a common difference 6 and the first term 10.

Hence A and E have the same sequence 10, 16, 22, .....

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Write the word sentence as an equation. Then solve.

The difference of a number n and 3 is -7.

Answers

Answer:

n-3 = -7

n = -4

Step-by-step explanation:

(Meeting character limit)

Answer:

-4

Step-by-step explanation:

n - 3 = -7, n = -4

if you multiply the number of cars in the parking lot by 4 there would be 32 cars how many cars are in the lot​?

Answers

If you do the steps backwards 32/4 is 8

Answer:

8

Step-by-step explanation:

there would be 8 cars in the parking lot

-PLEASE HURRY
8. Given: x2 – 2x + 5, find :
1.f(2)
2.f(-3)
3.f(0)
4.f(5) - f(-2)
5.f(1) + f(6)
-

Answers

Answer:

Step-by-step explanation:

     f(x) = x² - 2x + 5

1)   f(2) = (2)² - 2(2) + 5 = 5

2) f(-3) = (-3)² - 2(-3) + 5 = 20

3)  f(0) = (0)² - 2(0) + 5 = 5

4) f(5) - f(-2) = (5)² - 2(5) + 5 - [(-2)² - 2(-2) + 5 = 20 - 13 = 7

5) f(1) + f(6) = (1)² - 2(1) + 5 + [(6)² - 2(6) + 5 = 4 + 29 = 33

Need answer to the question

Answers

Answer:

B) Symmetric property of congruence

Step-by-step explanation:

The angles 1 and 2 are marked as congruent

If a ≅ b, then b ≅ a, this is called the symmetric property of congruence:

The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first.

Correct choice is B

Answer:

Symmetric property of similarity

Step-by-step explanation:

If a=a then that's reflexive propertyIf a=b and b=c then a=c, transitive property

I wish this was free ✋

Answers

Answer: It is tho ?

Step-by-step explanation:

Which situation can be represented by the expression 5.3d?
1. the total cost of an item that is d dollars more than $5.30
2.the total cost of d items that cost $5.30 each
3.the amount of change when $5.30 is used to pay for an item costing d dollars
4.the amount of change when $5.30 is used to pay for an item costing d dollars

Answers

Answer:

tang inamo ok please tell me

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