Answers
Answer: Choice A. [tex]\angle T[/tex]
Explanation:
Notice how letters Q and T are in the middle of the sequences of PQR and STR respectively. This means the angles correspond.
Because the triangles are congruent, this means the corresponding pieces are congruent. Therefore, angle Q and angle T are the same measure.
As you can see, the order matters when it comes to forming congruence statements. Something like [tex]\triangle PQR \cong \triangle STR[/tex] is slightly different from [tex]\triangle PQR \cong \triangle SRT[/tex]
Congruent triangles have all corresponding measurements like angles and side lengths congruent. The completed statement would be ∠Q ≅ ∠T (Option A: ∠T)
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[/tex] (small m shows we're taking about measurement) (both the statements are equivalent)[tex]\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E[/tex][tex]\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F[/tex][tex]\rm |AB| = |DE| \: \: or \: \: AB \cong DE[/tex][tex]\rm |AC| = |DF| \: \: or \: \: AC \cong DF[/tex][tex]\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex](|AB| denotes length of line segment AB, and so on for others).
For this case, we have: ΔPQR ≅ ΔSTR
Thus, we have:
[tex]\angle Q = \angle T[/tex]
Thus, the completed statement would be ∠Q ≅ ∠T. (Option A: ∠T)
Learn more about congruent triangles here:
https://brainly.com/question/16921692
Related Questions
In the figure, .
∠AEB and ∠CED are congruent
.
∠AEC and ∠
are congruent by the Vertical Angles Theorem.
Answers
Answer:
∠AEC ≅ ∠BED by vertical angles theorem
Answer:
Answer:
∠AEC ≅ ∠BED by vertical angles theorem
Step-by-step explanation:
If U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9); then
find(A-B)?
Answers
Answer:
{2, 4, 6, 8,10}
Step-by-step explanation:
GIven U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9);
Required
A-B = AnB'
B' = {2, 4, 6, 8,10}
AnB' are elements common to both A and B'.Hence;
AnB' = A- B = {2, 4, 6, 8,10}
Find the area of the circle shown Use pi=3.14
Answers
Answer:
50.24 sq cm
Step-by-step explanation:
radius is 4 (half of 8)
A=(3.14)4^2
A=50.24
Answer:
B) 50.24 sq.cm
Step-by-step explanation:
equation for area of circle is [tex]\pi r^{2}[/tex]
radius is half of diameter
radius = 4 cm
[tex]\pi (4)^2[/tex] = 50.24 sq.cm
Find the set of the possible values of p for which the equation 3x² + px + 3 = 0 has no real roots.
*Using graphical method or comparing the signs.
Answers
Answer:
[tex]delta = {b}^{2} - 4ac = {p}^{2} - 4 \times 3 \times 3 = {p}^{2} - 36[/tex]
The equation has no real roots if delta <0
that is -6<p<6
7.5 as an improper fraction in its simplest form
Answers
Answer:
7.5 as an improper fraction in its simplest form would be 15/2
Hannah lost four points on a test and earned four points on an extra credit question what does the sum of 0 mean in the description of this situation?
Answers
Answer:
Is that it's not about the answers and the questions
Use a substitution strategy to solve the following problem.
Two isosceles triangles have the same base length. The equal sides of one of the triangles
are 3 times as long as the equal sides of the other. Find the lengths of the sides of the triangles when
their perimeters are 34 cm and 82 cm.
Answers
Answer:
The length of the equal sides of the isosceles triangle with a perimeter of 34 cm perimeter is 12 cm
The length of the equal sides of the isosceles triangle with a perimeter of 82 cm perimeter is 36 cm
The base length of both triangles is 10 cm
Step-by-step explanation:
The given parameters are;
The base length of the triangles are equal
The base length of one of the triangle = The base length of the other triangle
The equal sides of one of the triangles = 3 × The length of the equal sides of the other
The perimeter of the triangles are; 34 cm and 82 cm
Let 'b' represent the base length of each triangle, let 'a' represent the length of an equal side of the smaller triangle with a perimeter of 34 cm and let 'c' represent the length of an equal side of the larger triangle with a perimeter of 82 cm
For the smaller triangle, we have;
b + 2·a = 34..(1)
For the other triangle;
b + 2·c = 82...(2)
Given that the side length of the larger triangle are larger than those of the smaller triangle, and that the side length of the larger triangle is 3 times the side length of the smaller triangle, we get;
c = 3·a
By the substitution method, from equation (2) we get;
b + 2·c = b + 2 × 3·a = b + 6·a = 82
∴ b + 6·a = 82...(3)
Subtracting equation (1) from equation (3) gives;
b + 6·a - (b + 2·a) = 82 - 34 = 48
b - b + 6·a - 2·a = 48
4·a = 48
a = 48/4 = 12
The length of the equal sides of the 34 cm perimeter (smaller) isosceles triangle, a = 12 cm
From c = 3·a, and a = 12, we get;
c = 3 × 12 = 36
The length of the equal sides of the 82 cm perimeter (larger) isosceles triangle, c = 36 cm
From equation (1), we get;
b + 2·a = 34
∴ b + 2 × 12 = 34
b = 34 - 2 × 12 = 10
The base length of both triangles, b = 10 cm
An angle is bisected, forming two new angels. If the original angle had a measure of 14 degree, what is the measure of each new angle
Answers
Answer:
The measure of each angle will be 7 degrees. It is because a bisector divides an angle in two equal halves. 14 / 2 = 7
Please help me figure out how to solve functions
Answers
Answer:
f(6) = 24
Step-by-step explanation:
To evaluate f(6) substitute x = 6 into f(x) , that is
f(6) = 6² - 2(6) = 36 - 12 = 24
Write 100 + 2 + 0.09 in standard form
Answers
Just add them up
Find the value of the variable that results in congruent triangles. Explain. SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)
Answers
well, let's keep in mind that the SAS postulate, so if one Side and the Angle next to it and the following Side after the angle are equal on both triangles, both triangles are congruent. Now, we have the angle 30° with sides and 9 and 2x and sides 9 and x + 4, well, the 9's are equal, dohh, you know, if only the 2x = x + 4, we'd be golden
[tex]2x = x + 4\implies 2x - x = 4\implies \boxed{x = 4}[/tex]
Proportions in similar triangles
Answers
Answer:
x = 4
Step-by-step explanation:
Given that DE is parallel to AC then DE divides the sides proportionally, so
[tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex] , substitute values
[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3x = 2(x + 2) ← distribute
3x = 2x + 4 ( subtract 2x from both sides )
x = 4
Thomas rents a car for his vaccation the milliage included with the 54 miles forer every mile he drives over 54 miles he needs to pay 5 integer 4 by 5 dollar if he drives 69 miles how much extra does he needed to pay
Answers
Answer:
$27
Step-by-step explanation:
Thomas rents a car for his vacation. The mileage include with the rental is 54 miles. For every mile he drives over 54 miles, he needs to pay $1 4/5. If he drives 69 miles, how much extra does he need to pay?
Total mileage included with the rental = 54 miles
Additional cost per mile after 54 miles = $1 4/5
Total miles Thomas drives = 69 miles
Extra miles Thomas drives = 69 miles - 54 miles
= 15 miles
how much extra does he need to pay?
Extra cost Thomas needs to pay = Additional cost per mile after 54 miles * Extra miles Thomas drives
= $1 4/5 * 15 miles
= 9/5 * 15
= (9 * 15) / 5
= 135/5
= 27
Extra cost Thomas needs to pay = $27
Irene faced north. She turned 270 ° to the left and then 90 ° more to the left.
In what direction is Irene now facing?
Answers
John turned in the following solution to an inequality and his teacher marked it wrong. What mistake did John make?
A. incorrectly reversed the inequality symbol
B. Failure to combine like terms
C. Incorrect division
D. Incorrect addition
Answers
Explanation when moving the +5 over with the -3, they said that -5-(-3) was -9, which is incorrect. It should be 2!
How much is -1/4 is 1 1/3?
Answers
Answer:
4 option
Step-by-step explanation:
Solve this please!!,!,!
Answers
Answer:
z = -74
Step-by-step explanation:
12 = (2+z) / -6
Multiply each side by -6
-6 * 12 = (2+z)/ -6 * -6
-72 = 2+z
Subtract 2 from each side
-72-2 = 2+z-2
-74 =z
2 Kenedi has a piece of ribbon that measures
24 inches long. She cuts the ribbon into
15 equal pieces to attach to her dance
costume. Kenedi uses the expression shown to
calculate the length of each piece of ribbon she
uses on her costume.
241 - 15
Which of the following expressions CANNOT be
used to determine the length of each piece of
ribbon?
15
F99=
G (242) (15)
H7+15
J 241-15
Answers
Answer:
The length of each ribbon is 1.6 inches
Step-by-step explanation:
From the question, we are told that:
Kenedi has a piece of ribbon that measures 24 inches long. She cuts the ribbon into 15 equal pieces to attach to her dance costume
Hence, the expression that can be used to show how to calculate the length of each piece of ribbon is given as:
24 inches ÷ 15 pieces
= 24 ÷ 15
= 1.6 inches
Therefore, the length of each ribbon is 1.6 inches
A 6) Set both given equations equal to zero, then combine them into one standard form
equation. Simplify if possible.
7x + 3 = 5 and y-1 = 6
Answers
Answer:
The standard equation is 7x + y = 9
Step-by-step explanation:
Equations given are:
7x + 3 = 5 and y - 1 = 6
Set both given equations equal to zero, then combine them into one standard form equation
Set the equations to zero by moving the constant from R.H.S to L.H.S
7x + 3 - 5 = 0
7x - 2 = 0 ---- eq 1
y - 1 = 6
y - 1 - 6 = 0
y - 7 = 0 ----- eq 2
We have to combine eq 1 and eq 2
7x - 2 + y - 7 = 0
7x + y - 9 = 0
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Thus the standard equation is:
7x + y - 9 = 0
7x + y = 9
Thus the standard equation is 7x + y = 9
In a school 640 teachers like either milk or curd or both . The ratio of number of twacher who like milk to the number pf teachers who like curd is 3:2 and 160 teachers like both milk and curd . Find: How many teachers like milk?& How many teachers like curd only.
Answers
3+2=5
Milk =3/5×640 = 384
Curd 2/5×640 = 256
PLEASE HELP WILL MARK BRAINLIEST
Answers
Find the area of this prism.
Answers
240 cubic centimeters.
Just use the formula length x width x height
And divide the figure into two figures so u can find the area much easier
Comm.ent me if u have any questions,
-SpaceMarsh
Brainliest pls?
1) The population of Leafy Lake starts at 3,000 and grows by 25% every year. What will the population be in 6 years?
how do I solve it
Answers
100x = 3,000x25
100x = 75,000
100x/100 = 75,000/100
X = 750
750x6 = 4,500
Every year the population goes up by 750, in 6 years the population would be 4,500 people.
Answer:
Step-by-step explanation:
Rate of increase = r = 25%
n = number of years = 6
P = Current population = 3000
Population after n years = [tex]P*(1 + \frac{r}{100})^{n}[/tex]
[tex]= 3000 * (1 +0.25)^{6}\\\\= 3000 * (1.25)^{6}\\\\= 3000 * 3.8\\\\= 11400=[/tex]
Sally plots (−4,π)on the polar plane.
How does she proceed?
Drag a phrase to each box to correctly complete the statements.
Answers
Solution :
As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.
My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.
someone help me with this
Answers
Answer:
stars: triangles
3 : 1
Step-by-step explanation:
There are 3 starts and 1 triangle
stars: triangles
3 : 1
Answer:
3:1
Step-by-step explanation:
3 Stars and 1 Triangle
AC = 16, AB = x + 1, and BC = x + 7. What is the measure of the length of AB? HELP
Answers
Answer:
5
Step-by-step explanation:
AC=AB+BC
so 16=x+1+x+7
which simplifies to 16=2x+8
subtract eight from both sides to get 8=2x
then divide by 2 to get that x=4
AB=x+1, which substitutes into 4+1=5
Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of m and n.
Answers
Answer:
m = 3 , n = 4
Step-by-step explanation:
Using Section Formula.
[tex]If \ the \ line \ segment \ AB \ where \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \ the \ points \ of \ P \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}[/tex]
[tex]Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x = -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3[/tex]
[tex]y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4[/tex]
Find f(x+2) of the function f(x)= 4x^2+2x-4 HELP ASAP PLEASE WORTH 40 POINTS
Answers
Answer:
Given
f(x)= 4x²+2x-4To find f(x + 2) substitute x with x + 2 in the given function:
f(x+2)= 4(x + 2)² + 2(x + 2) - 4
= 4(x² + 4x + 4) + 2x + 4 - 4
= 4x² + 16x + 16 + 2x
= 4x² + 18x + 16
f(x+2)
4(x+2)²+2(x+2)-44(x²+4x+4)+2x-4-44x²+16x+16+2x4x²+18x+16don't mind the purple dot
Answers
Answer:
option A
Step-by-step explanation:
22 : 15 + 10hours = 8 : 15
8 : 15 + 35 minutes = 8 : 50
Therefore the difference = 10 hours 35 minutes
HELP
Find the circumference of this circle
using 3 for T.
C [?]
Answers
Answer:
3
Step-by-step explanation:
3