Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent. To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed? ∠DEF ≅ ∠ DGF ∠DFE ≅ ∠ DFG DE ≅ DG DG ≅ GF
Answers
Answer:
[tex]\angle DFE = \angle DFG[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What makes DEF and DGF congruent
We have:
[tex]EF = GF[/tex] --- this is indicated by the single line on both sides
Also:
[tex]DF = DF[/tex] --- both triangle share same side
For SAS to be true;
2 sides and 1 angle must be equal in either triangles
So far, we have:
[tex]EF = GF[/tex] ---- S
[tex]DF = DF[/tex] ---- S
The additional to complete the proof is:
[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides
Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.
Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.
The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.
So that,
GF ≅ FE (given)
DF is the common side to triangles DEF and DFG.
DFG is the included side.
Thus;
∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)
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Related Questions
if John and Eric bought a large pizza that has 10 slices John and Eric it all the pizza if John ate 1/5 slice how many did Eric eat
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which point is a solution to y>2x-1?
Answers
Answer:
B) (0,2)
Step-by-step explanation:
We substitute the values of x and y into this inequality:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
This is true, so this is the correct point
hope this helps have a good day
Answer:
there it is
Step-by-step explanation:
plzzz help
thank u for those who help
Answers
Answer:
SAS
Step-by-step explanation:
As per the given diagram, the following facts are evident.
(BR) = (CR), Both sides have two small orange lines on them. This shows that these sides are congruent.
(<B) = (<C), this is shown by the box around both angles, indicating that both angles have a measure of (90) degrees.
(AB) = (AC), Both sides have one small orange line on them. This indicates that these sides are congruent to each other.
Therefore, the sides are congruent by the theorem (SAS); side-angle-side, congruence.
(PLS HELP NOW WILL GIVE BRINIEST!!!!!) A figure is formed by two pairs of parallel sides that are the same length. Which type of figure is it?
A.
hexagon
B.
square
C.
pentagon
D.
triangle
Answers
Answer: B. Square
Step-by-step explanation:
All sides of a square have the same lengthAll four angles of a square = 90°A square has two parallel sidesThe answer is B.), because if you have two pairs of parallel sides that means it looks like a square 1. || 2. _
_
- Chilio
please help a and b
Answers
Answer:
a=144.15
median=157.5
f equals to 2 f - 20
Answers
Answer:
20
Step-by-step explanation:
f = 2f - 20
f - 2f = - 20
- f = - 20
f = 20
A right triangle has one angle that measures 70 degrees what is the measure of the other acute triangle
Answers
Answer:
20
Step-by-step explanation:
180 - 90 - 70 = 20
The sum of all angles in a triangle equals 180.
Triangle Sum Theory
One number is 6 times a second number. The sum of the two numbers is 56. Find the numbersOne number is 6 times a second number.
The sum of the two numbers is 56. Find the numbers
Answers
Answer:
I think its 56 = 56
Step-by-step explanation:
Answer:
8 and 48
Step-by-step explanation:
This can be written as a system of equations. X will be the smaller number and y will be the larger:
6x = y
x + y = 56
Then substitute y in the second equation for 6x(seen in first equation) and solve.
x + 6x = 56
7x = 56
x = 8
So one number is 8. To find the other plug in 8 for x in either of the original equations (both get the same answer for y).
6x = y
6 * 8 = y
48 = y
Then double check by seeing if they fit the requirements of the problem.
Hope this helps!
the LCM of 16 and 18 is
Answers
the lcm of 16 and 18 is 144 !
Can someone please help me. If you do thanks
Answers
Answer:
(B)
Step-by-step explanation:
Can't explain lol, but that's the answer
What is the slope and y-intercept of the following equation:
= 13 − 4 (show your work pls)
Answers
Answer:
Slope is 1/3
Y intercept is -4
need a help!!!
I need the answer only for the c part
Please help!!
Please answer correctly
Answers
Step-by-step explanation:
316 days when you get the idea the most important thing is that the people who are looking for the right reasons why you
x + y = 3, 4y = -4x - 4
System of Equations
Answers
Answer:
no solutions
Step-by-step explanation:
Hi there!
We're given this system of equations:
x+y=3
4y=-4x-4
and we need to solve it (find the point where the lines intersect, as these are linear equations)
let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable
we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4
y=-x-1
now we have y set as an expression containing x
substitute -x-1 as y in x+y=3 to solve for x
x+-x-1=3
combine like terms
-1=3
This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.
Therefore the answer is no solutions
Hope this helps! :)
The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution
One group of new freshmen is given a study-skills training course during the first week of college and a second group does not receive the course. At the end of the semester, the grade point average is recorded for each student. For this study, what is the dependent variable
Answers
Answer:
The dependent variable is the grade point average recorded for each student.
Step-by-step explanation:
The dependent variable is defined as the variable that is to be tested or even measured in an experiment.
In this question, At the end of the semester, the variable that is being tested is the grade point average for each student.
Thus it is the dependent variable.
Solve for x. Round to the nearest tenth, if necessary.
Answers
COS= ADJ/HYP
COS(61)= 5.5/X
Final answer:
X= 5.5/COS(61)
X= 0.1 [rounded to nearest tenth]
2m^2-5m-3=0 by factorization
Answers
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
Instructions: Find the measure of
Answers
Answer:
93
Step-by-step explanation:
Add the two angles 48 and 39 =87. 180-87=93
Find the measure of ∠AED for m∠BEC = 118
Answers
Answer: 118°
Step-by-step explanation:
Juan is selling fruit baskets and pencils for his
fundraisers. He started his fundraising early and has 12
weeks to reach his goal of selling $300.00 worth of
goods to pay for his trip's cost.
If Juan uses the table shown to represent all of his
data, what interval for the weeks would you use in
column 1 so that all 12 weeks are represented?
Week.labels:
X1, 2, 3, 4
2, 4, 6, 8
3, 6, 9, 12
1, 3, 6, 10
Answers
Answer:
Juan will need the number of fruit baskets to sell the last three weeks to achieve his goal=18
Step-by-step explanation:
sszhskf7kj Is correct
He's the one that commented on the other answer
C) 3, 6, 9, 12
probability of multiple events
A standard number die is tossed once, and then again. Find P(first
roll = 1 and second roll = 1),
help pls
Answers
Answer:
1/36
Step-by-step explanation:
A standard die has 6 faces
The numbers 1 through 6 on singly on each face
so the probability of tossing a 1 would be;
1/6
The probability of tossing another 1 would still be same 1/6
So the probability of tossing a 1 and another 1 would be the product of the two tosses as follows;
1/6 * 1/6 = 1/36
Simple percent question!!!!
My question says that line segment DC is 50% longer than line segment BD, and BD is 40 ft. Does that mean DC is 60 ft or 80? Please explain, brainliest to whoever explains it properly and quickly
Answers
Answer:
60ft
Step-by-step explanation:
DC is 50% longer than BD (given)
BD is 40ft (given)
DC is 50% longer than BD this means that DC= BD+50% of BD
40ft +50/100 * 40
=40ft +20ft
=60ft
Another way to solve this could be DC is 150%of BD as BD =40ft=100% of it's length.
So, 150/100 *40
=60ft
Hope this helps.
Please mark me as brainliest.
Pls help this set question
Answers
1: True
2: False
3: False
4: True
5: False
6: True
sue has 18 pieces of candy
tony has 18 pieces of candy
sue then gives some to tony
sue then eats five of hers
tony eats half of his
write the expressions for the number of pieces candy sue and tony now have?
Answers
Answer:
Sue candy = 13 - x
Tony candy = 9 + 1/2x
Step-by-step explanation:
Sue candy = 18
Tony candy = 18
Let x = some candy gives to tony
Sue candy = 18 - x
Tony candy = 18 + x
sue then eats five of hers
Sue candy = 18 - x - 5
= 13 - x
tony eats half of his
Tony candy = 1/2(18 + x)
= 18/2 + x/2
= 9 + 1/2x
Expressions for the number of pieces candy sue and tony now have:
Sue candy = 13 - x
Tony candy = 9 + 1/2x
the diagram shows a square with perimeter 20cm
work out the percentage of the area shaded inside the square that is shaded
Answers
Answer:
70%
Step-by-step explanation:
Finding each side :-
4a = 20ma = 5 mFinding area of unshaded region :-
A = 1/2 * b * h A = 1/2 * 1.5 * 5 cm² A = 2.5 * 1.5 cm²A = 3.75 cm² Total unshaded region = 2*3.75 = 7.5 cm²Overall area :-
A = a²A = (5cm)²A = 25m²Finding percentage :-
% = 25 - 7.5 / 25 * 100 % = 17.5 * 4 % = 70Answer:70%
Step-by-step explanation:
Complete the remainder of the table for the given function rule: y= x/4 + 7
Answers
Let's replace x with -4 and simplify
y = (x/4) + 7
y = (-4/4) + 7
y = -1 + 7
y = 6
This means x = -4 and y = 6 pair up together.
So 6 goes in the box under the -4
----------------------------------------------------------
Repeat those steps for x = 0
y = (x/4) + 7
y = (0/4) + 7
y = 0 + 7
y = 7
So 7 goes in the box under the 0
----------------------------------------------------------
Let's repeat those steps for x = 4
y = (x/4) + 7
y = (4/4) + 7
y = 1 + 7
y = 8
So 8 goes in the box under the 4
----------------------------------------------------------
Lastly, for x = 8, we get
y = (x/4) + 7
y = (8/4) + 7
y = 2 + 7
y = 9
9 goes in the box under the 8
----------------------------------------------------------
The y outputs we got were: 6, 7, 8, 9
Notice how each time y increases by 1, x goes up by 4.
This means slope = rise/run = 1/4
We can think of x/4 as (1/4)x to help see that the slope is 1/4.
A function assigns the values. The value of the y in the given table should be 6, 7, 8, and 9, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function of the x and y is given y=(x/4)+7, use this function to find the value of y for the given values of x. Thus,
x = -4
y = (-4/4)+7
y = -1+7
y = 6
x = 0
y = (0/4)+7
y = 7
x = 4
y = (4/4)+7
y = 8
x = 8
y=(8/4)+7
y = 9
Hence, the value of the y in the given table should be 6, 7, 8, and 9, respectively.
Learn more about Function:
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The number of strokes in which a hole is designed to be played. [ Choose ] The person who is farthest away from the hole is said to have _____.
Answers
Answer:
the answer is more strokes since the farther away you are the more strokes it takes
Hope This Helps!!!
the vector a,b and c are given as a=2i+3j-4k. b =5i+3j+7k. c =6i+2j-k
find 1)a-2b+4c
2)5a+2b-c
Answers
???????????????????????????
Answers
Answer: its 20 I think
Answer:
x = 50
I hope this help the side note also help me a lot as well
If line n bisects CE, find CD.
Answers
If it bisect, then using the Line Bisector Theorem, it must be equal.
So x+6=4x-21
get like terms on 1 side
x+6=4x-21
-x. +21
27= 3x
x=9
plug the x in
CD= 9+6
CD=15
The value of CD such that line n is bisecting line segment CE is 15.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given that line, n is bisecting the line segment CE at D
CD = DE
Given CD = x + 6 and DE = 4x - 21
x + 6 = 4x - 21
4x - 21 = x + 6
4x - x = 6 + 21
3x = 27
x = 9
Therefore CD = 9 + 6 = 15
Hence "The value of CD such that line n is bisecting line segment CE is 15".
For more about line segments,
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i need the answer asap please help!
