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
Answers
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 = ∠ODAReasons:
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
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.
help me plssssssssssssss
Answers
multipley by 2, to get the answer
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.)
Help help math math math
Answers
thank u
Answer:
-3/7,0
Step-by-step explanation:
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
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
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
I wish this was free ✋
Answers
Answer: It is tho ?
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.
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 graphStep 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:
-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
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:
I want a way to solve such a problem
Answers
Answer:
11.2
Step-by-step explanation:
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
Answer:
8
Step-by-step explanation:
there would be 8 cars in the parking lot
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
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
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.
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
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
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
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
Need answer to the question
Answers
Answer:
B) Symmetric property of congruenceStep-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 property3. 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]
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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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
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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Which property explains why these two expressions are equal? 7 + q + 4 = 4 + 7 + q
Answers
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
PLEASE HELP WILL MARK BRAINLIEST!
Answers
Answer:
Step-by-step explanation:
[tex]12000(1+\frac{.12}{4})^{4*45}=2454040.31463\\=2454040[/tex]
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
solve systems of equations 6x+2y=1 y=-3x+3 using substition??? Need answers quickly!!!!!