Ketki and Kunal are playing a game where they are making triangles in different scenarios.
In which of the following situation the triangles made by them would be congruent?
( i ) Both making a triangle FUN with side FU=4cm and angle F= 60º
( ii ) Both making an equilateral triangle ARE.
( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cm
( iv ) Both making triangle DIP with all angles equal.
Answers
The situation in which triangles will be made congruent for sure is given by: Option ( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cm
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
For two triangles being congruent, we need at least:
Either, 3 corresponding side pairs are congruent. (SSS congruency), Or, any 2 corresponding sides and angle between them are congruent. (SAS congruency).Or, any 1 side of same measurement as its corresponding side in other triangle with two angles on its endpoints of same measurement as per their corresponding angles in the other triangle. (ASA congruency).Checking all the options:
( i ) Both making a triangle FUN with side FU=4cm and angle F= 60ºOnly one side and one angle are not enough.
( ii ) Both making an equilateral triangle ARE.Two equilateral triangles are not necessary to be congruent. Example, one equilateral triangle has sides of 3 units, and other triangle has sides of 5 units.
( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cmTwo sides TR and RY and a non-included angle T is given. This doesn't satisfy SAS' condition. But since it is given that:
Angle T is right angled, so we now know that RY is going to be hypotenuse.
Using this fact, and the fact that |RY| = 5 cm, |TR| = 4 cm, and Pythagoras theorem, we can get |TY| = 3 cm.
Thus, it will complete SSS condition, and therefore, by SSS congruency, the triangles made in this case would be congruent.
( iv ) Both making triangle DIP with all angles equal.All angles(corresponding) being equal implies similarity, but not congruence.
Thus, the situation in which triangles will be made congruent for sure is given by: Option ( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cm
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Related Questions
Give the equation of the circle centered at the origin with radius 3.
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please help find x and mDE
Answers
Answer:
x = 16
measure of Arc(DE) = 167°
Step-by-step explanation:
Since the arc EFG make a straight angle, we can infer;
180° = Arc(EF) + Arc(FG)
180° = (x-3)° + (12x - 25)°
180° = 13x - 28
208 = 13x
16 = x
Arc GF and DE are vertical angles so if you find the measure of Arc GF then it's the same as measure of Arc DE
mDE = mGF
mDE = 12x - 25
mDE = 12(16) - 25
mDE = 192 - 25
mDE = 167°
Hope this helps!
Work out the area of the shape drawn below.
6 m
Answers
Answer:
28.3 m²
Step-by-step explanation:
The formula to find the area of a quadrant: 1/4 x π x r², where r is radius (diameter ÷ 2) and π is 3.14 or 22/7 or 3.142.
1) Substitute the values into the formula.
= 1/4 x 22/7 x 6²
2) Solve it.
= 1/4 x 22/7 x 36
= 1/4 x 113.14
= 28.285
2) Round the answer to one decimal place.
= 28.3
Joyce paid $38.50 for an item at the store that was 65 percent off the original price. What was the original price?
Answers
Answer:
25.025
Step-by-step explanation:
x/38.50=65\100 cross multiply and divide by the 100 so now x=Original price=25.025
Here are the results of a survey of 525 people in a town.
• 135 females speak Welsh.
• 163 males do not speak Welsh.
• 238 people do not speak Welsh.
Use the results of the survey to work out the ratio
males in town who speak Welsh : males in town
Answers
287-135 = 152 males speak welsh
238-163 = 75 females do not speak welsh
135+75 = 210 total females
525-210= 315 total males
152/315= 0.48 ~~ 48%
Which of the following is a root of the polynomial function below?
F(x) = x2-3x2+x+5
O A. -2+1
O B. 2
O C. 2+1
O D. 1
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Reemplaza los valores en las expresiones y resuelve
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Substitute values into expressions and solve??
select the place where the digit 2 sits in this number 428,031
Answers
Answer:
The 2 is in the ten thousands place.
Answer:
In this case the number 2 would be located in the tens of thousands.
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I hope help you :)
Kind regards, Antonio.
by first rounding each number to 1 significant figure, estimate the answer to 427+941
Answers
Answer:
1300
Step-by-step explanation:
How much would
$550 invested at 9%
interest compounded
annually be worth
after 8 years?
Answers
After 8 years the worth would become $1,095.91
How to find the compound interest?If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that $550 invested at 9% interest compounded annually be worth after 8 years.
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
a = 550 (1 + 0.09)^8t
a = 550 (1.09)^8t
a =1,095.91
Hence, the worth would be; $1,095.91
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pls answer me thus question
Answers
Answer:
iii is the correct answer (the third one)
Step-by-step explanation:
additive inverse is the same as the reciprocal
It is when the denominator and numerator are swapped around
So the inverse of 3/9 is 9/3
Brainliest would be appreciated
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Answer:
I don't really know but I'm curious haha
Help picture below problem 23
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Answer: 7 hours.
Step-by-step explanation: Randall can assemble 5 race car tracks in an hour and Diggery can assemble 4 race car tracks in an hour. To see how many hours it takes to make 63 race car tracks, you need to add 5 and 4, since Randall and Diggery are working together. Both of them combined can make 9 race car tracks in total every hour. 63 can be divided by 9, which is 7. Therefore, it'll take 7 hours for both of them to make 63 race car tracks.
Let me know if this is right! :)
Help help math math math
Answers
Answer:
1) 13
2) 9
3) 5
4) 1
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
Answer:
13, 9, 5, 1
Step-by-step explanation:
all you have to do is plug in the x to find the y
How many cups of mashed potatoes were four people get if they equally shared 3/4 cup of potato
Answers
Answer:
3/4 x 2 = 6/8 6/8 ÷ 4 = 2/8
so each person would get 2/8 cups of potatoes
Which is a step in the process of calculating successive discounts of 8% and 10% on a $50 item?
a. take 2% of $50
b. take 8% of $46
c. take 10% of $46
d. take 18% of $50
Answers
Answer:
C. take 10% of $46
Step-by-step explanation:
Hope this helps you! :)
A right square pyramid is shown. The height of the pyramid is 40 units. The distance from the center of the base of the pyramid to vertex D is 30units, as shown.
Enter the length of segment AD, in units
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Answer:
c=a2+b2
use the Pythagorean Theorem
Select all the correct locations on the image. Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
Answers
The parabolae b, d and f seen in the real coordinate plane have complex roots.
What is the graphical criterion to determine what second order polynomial has complex roots?
Second order polynomials are algebraic equations of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
a, b, c - Coefficientsx - Independent variabley - Dependent variableA value of x is a root of the polynomial for y = 0, which can real or complex but not both according to the discriminant of the quadratic formula. If the polynomial has no real roots, then it does not pass through the x-axis in the real coordinate plane.
Therefore, the parabolae b, d and f seen in the real coordinate plane have complex roots. [tex]\blacksquare[/tex]
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Your invest $88,000 a CD that is locked into a 1.75% interest rate compounded monthly for seven years how much will Urich have an account with the CD matures
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$88000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=88000\left(1+\frac{0.0175}{12}\right)^{12\cdot 7}\implies A=88000\left( \frac{4807}{4800}\right)^{84}\implies A\approx 99459.21[/tex]
Construct the indicated confidence interval for the population mean using the t-distribution. Assume the population is normally distributed.
picture of question below
Answers
Order these numbers from least to greatest.
7.773, 157/20, 7.77, 7 9/11
Answers
Answer:
7.77, 7.773, 7 9/11, 157/20
Step-by-step explanation:
First, convert any fractions to decimals to make it a bit easier to order.
7.773, 157/20, 7.77, 7 9/11
157/20 = 7.857 9/11 => 86/11 => 7.82Now we have:
7.773, 7.85, 7.77, 7.82
Order from least to greatest:
7.77, 7.773, 7.82, 7.85
Rewrite using the original numbers in the question:
7.77, 7.773, 7 9/11, 157/20
Hope this helps!
"Describe the domain and range of y=5(2)"
Answers
Answer:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞), {x|x∈R}
Range: {y|y=10}
(I apologize if this doesnt help)
James and his family spend a morning picking peaches. They fill several bags. This line plot shows the weight of each bag.
How many more pounds does one of the heaviest bags weigh than one of the lightest bags?
Answers
The number of pounds that one of the heaviest bag weighs more than one of the lightest bag in the given line plot is: 1½
What is a Line Plot?In a line plot, frequency of a data point is either represented by a dot or a mark.
In the line plot given:
Heaviest bag weighs 5¾
Lightest bag weighs 4¼
The difference between the heaviest and lightest bag = 5¾ - 4¼
= 23/4 - 17/4
= (23 - 17)/4 = 6/4 = 3/2
= 1½
The heaviest bag weighs 1½ pounds than the lightest bag.
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Which transformation below causes Figure A to transform into Figure A’?
A. a reflection across the y-axis
B.a reflection across the x-axis
C.a clockwise rotation of 90 degrees about the origin D.a translation 12 units right and 2 units down
Answers
Answer:
D.a translation 12 units right and 2 units down
Answer:
D
Step-by-step explanation:
If you take one of the point and compare it to the corresponding one on the second triangle, you can see that it is a translation of 12 right 2 down.
Find the perimeter of the figure below. Show all work for each step. Work should include explanations in words detailing how you simplify each specific radical. Take your time and be thorough. Include units in final answer.
Answers
Applying the knowledge of radicals, the perimeter of the given triangle is calculated as: 63√6 cm
What is the Perimeter of a Triangle?To find the perimeter of a triangle, add up the length of all its three sides.
Given the trangle in the image:
Perimeter = 12√54 + 15√6 + 6√24
Simplify each radicals
12√(9 × 6) + 15√6 + 6√(4 × 6)
12 × 3√6 + 15√6 + 6 × 2√6
36√6 + 15√6 + 12√6
Add like radicals together
Perimeter = 63√6 cm
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Which object would have a measurable volume? A bunch of polaroid pictures. A beach ball. A sheet of loose leaf paper. A checker board.
Help!!
Answers
Answer:
its ethier the photo or the beach ball but i dont know which is
Step-by-step explanation:
Answer:A beach ball.
Step-by-step explanation:
A team from the high school went on a science-and-math quiz show. The science questions were worth 3 points and the math questions were worth 1 point. The team answered a total of 16 questions and earned 36 points. How many questions did the team answer in each category?
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Answer:
5 science questions and 1 math question
Step-by-step explanation:
i literally just counted on my fingers by 3
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Answer:
6000 lbs is greater then 5000!
Step-by-step explanation:
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Step-by-step explanation:
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