Given that ABCD is a parallelogram with diagonals intersecting at M. Segment PQ is drawn such that P lies on AB and Q lies on DC and it passes through M. Prove that PM is congruent to QM.
Answers
Answer:
we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and
PM = QM
Step-by-step explanation:
because it's a parrallelogram, Ad = BC and AB = DC.
P passes through both AB and DC on a diagonal, angles created by P have oppoiste exterior angles of eachother.
the diagonals of AC create congruent angles at DMC and AMB and because P is cutting through them, the angles P cuts at DMQ and QMC are equal to that of AMP and PMB
that being said, we now see that the angles of APM triangle and AMC triangol are equal and because the diagonal of BD is is being cut by AC, which AD is parralel to BC and AB to Dc, we know now that lines AM and MC are congruent
we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and
thus PM = QM
The alternate interior angles formed by the parallel sides and a common
transversal are equal, such that ΔPBM and ΔQDM are congruent.
Correct response;
PM is congruent to QM by CPCTCHow is the congruency of the segments determined?The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ABCD is a parallelogram [tex]{}[/tex] Given
AC and DB are diagonals of ABCD [tex]{}[/tex] Given[tex]{}[/tex]
M is the point of intersection of the diagonals [tex]{}[/tex] Given
MB ≅ DM, and AM ≅ CM;[tex]{}[/tex] Properties of the diagonals of a parallelogram
∠PMB ≅ ∠DMQ [tex]{}[/tex] Vertical angles theorem
∠PBM ≅ ∠QDM [tex]{}[/tex] Alternate interior angles theorem
ΔPBM ≅ ΔQDM [tex]{}[/tex] Angle-Side-Angle Congruency post.
PM ≅ QM [tex]{}[/tex] CPCTC
ΔPBM is congruent to ΔQDM by Angle-Side-Angle congruency
postulate, given that they have two angles and an included side that are
congruent.
Therefore;
PM is congruent to QM by Corresponding Parts of Congruent Triangles are Congruent, CPCTC.Learn more about congruency postulates here:
https://brainly.com/question/17003791
Related Questions
plz help i will give brainiest
Answers
Answer:
So I'm guessing its
x| -7, -6, -5, -4, -3
y| -2, 1, 4, 1, 2
Step-by-step explanation:
The answer I got was its a vertex. so yeah. and I think you just put the -2 on the Y
NEED HELP ASAP PLEASE
[tex](4 {c}^{2} - + 15c + 18) \div (c + 2)[/tex]
Answers
I hope this help
There are cows and turkeys at a farm, 82 heads and 264 legs in all. There is no need to explain that a cow has four legs, while a turkey has two legs. How many cows and turkeys are at the farm? How can I solve this using elimination or substitution can I have steps please. No spamming please
Answers
Cows+turkeys=82
4 cow legs + 2 turkey legs = 264
C+T=82
-T. -T
—————
C= 82-T wherever you see a “C” substitute this formula
4C+ 2T=264
4(82-T)+ 2T=264
(82*4)- (4T+2T)= 264
328-2T=264
-328. -328
————————
-2T= -64
-2T/-2= -64/ -2
T=32 there are 32 turkeys
There are 82 heads total
If we know there are 32 turkeys then the rest have to be cows.
82-32=50
Hope this helps!
HHHeeelllp please sos
Answers
Answer:
30 degrees
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
Find the missing value need help
Answers
Answer:
-10 +5
its +5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
i just know it
solve for x and the measures for
x=4
Answers
Answer:
Below in bold.
Step-by-step explanation:
The angles on the line AC add up to 180 degrees, so:
11x - 8 + 90 + 6x + 2 + 4x + 12 = 180
21x + 96 = 180
21x = 180 - 96 = 84
x = 84/21
x = 4.
<ABD = 11(4) - 8 = 36 degrees.
<EBF = 6(4) + 2 = 26 degrees.
<CBF = 4(4) + 12 = 28 degrees.
estimate the value of 196/0.499
Answers
Answer:
788
Step-by-step explanation:
Answer:
392.785 or 392.79
Step-by-step explanation:
(x - 3)2 + (y + 2)2 = 4
Answers
Answer:
x = -y + 3
y = -x + 3
In standard form, it would be 2x + 2y = 6
Help me please explain how you did it too
Answers
Answer:
$112
Step-by-step explanation:
$168 per 12 hours of work
168/12 = 14
$14 per hour of work
14*8 = 112
$112 per 8 hours of work
I hope that this helped
168/12=14 . 14•8= 112
i am pretty sure this is the answer
Will mark Brainliest!!!!
the three are
perpendicular
parallel
neither parallel nor perpendicular
Answers
Answer:
ParallelNeither parallel nor perpendicular PerpendicularStep-by-step explanation:
Given line m:
y = 4/5x - 3Relationship of line m with following lines:
1. y = 4/5x + 3
Same slope, different y-interceptParallel2. y = -4/5x + 3
Slope are negative, different y-intercept Neither parallel nor perpendicular 3. y = - 5/4x + 3
Slopes are negative-reciprocal, different y-interceptPerpendicularConsider parallelogram ABCD. If AC¯¯¯¯¯¯¯¯=2x+15 and BD¯¯¯¯¯¯¯¯=5x−12, what does the value of x need to be so that the parallelogram is a rectangle?
A: 1
B: -9
C: 9
D: 3/7
Answers
Answer:
9
Step-by-step explanation:
I took the quick check
find the mode, median, mean, and range of 3, 7, 2, 4, 7, 5, 7, 1, 8, 8
Answers
Median-6
Mean-5.2
Range-7
Answer:
Mean = 5.2
Mode = 7
Median = 6
Range = 7
Step-by-step explanation:
Mean is all 10 numbers added up divided by 10
Mode is 7 s it is the most common integer
Median is 6 as it is the middle number between 5 and 7 and 7+5/2 = 6
Range is 7 as 8-1 is 7
Hope this helps :)
f(t) = 2t - 3
f(1) =
Answers
A company is designing a new cylindrical water bottle. The volume of the bottle will be 99 cm³. The height of the water bottle is 7.8 cm what is the radius of the water bottle. Use 3.14 for
Answers
Answer:
2.08
Step-by-step explanation:
99/7.8=13.56
13.56/3.14=4.32
the square root of 4.32 is 2.08
How many wholes are in 21/5?
Answers
4.2
hope it help u
plzfollow me
what is 4.059 divided by 100
Answers
Answer:
0.04059
Step-by-step explanation:
If 5 boxes of girl scout cookies cost $20, how many boxes of girl scout cookies can I buy for $36?
Answers
Answer:
9
Step-by-step explanation:
20 / 5 = 4 36 / 4 = 9
I am going to break into ur house if you dont answer my Higher Order Thinking Question (lol)
In a company, 60% of the workers are men. If 1380 women work at the company, how many workers are there total? Show (type) two ways that you can solve this problemo.
Answers
Answer:
2208 is how many workers total
Step-by-step explanation:
Ima only give one way bc I only know one lol so what you do is you multiply 1380 by 60% which is 828 and then you add that to 1380 and you get 2208
8x - 14y = 3
Slope intercept form
Answers
Step-by-step explanation:
y= -8/14x + 3/14 is the answer
Answer:
y=1.75x-3/14
Step-by-step explanation:
-14y=-8x+3
y=14/8x-3/14
y=1.75x-3/14
find the y and x intercept for
4x-y=12
Answers
Answer:
x intercept: (3,0)
y intercept: (0, -12)
Tommy's bank requires a $150
minimum balance. Unfortunately,
he is overdrawn by $27. How much
does he need to deposit in order to
meet the minimum requirement?
Answers
Answer:
$27
Step-by-step explanation:
I really don't know but my beest guess would be $27 to get back to $150.
Answer:
177
Step-by-step explanation:
All you need to do is add.
State the number of solutions (One Solution, No Solution, or Infinitely Many) for each system
(2x + y = 2
2x + y = 8
(y = 3x - 7
7.
8.
9.
ly-2=-2x
3x + 5y = 5
y = 3x+2
Answers
The sum of two number is 65 and their difference is 5.Set up and solve a system of equations to find the two number.Show work
Answers
Answer:
it 60
Step-by-step explanation:
60
5x^2-41x+8=0 please helpp
Answers
Answer:
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
5
2
−
4
1
+
8
=
0
5x^{2}-41x+8=0
5x2−41x+8=0
=
5
a={\color{#c92786}{5}}
a=5
=
−
4
1
b={\color{#e8710a}{-41}}
b=−41
=
8
c={\color{#129eaf}{8}}
c=8
=
−
(
−
4
1
)
±
(
−
4
1
)
2
−
4
⋅
5
⋅
8
√
2
⋅
5
2
Simplify
3
Separate the equations
4
Solve
Solution
=
8
=
1
5
X= 1/5 is solution
help?? please i need it
Answers
Answer:
I think the answer is no because none of these are divisible by any of the numbers
pls help has to be in a fraction ill give brainliest.
Answers
Answer:
-5/4
Step-by-step explanation:
slope = -4 - (-29) / -10 - 10
slope = 25 / -20
slope = -5/4
The lowest point on the Earth's surface is in the Mariana Trench in the
Pacific Ocean. It has a depth of about 36,069 feet. Which is this depth
written in scientific notation?
A 36 x 103
B 3.6 x 104
C 3.6 x 105
D 0.36 x 105
PLEASE HELP MEEE!
Answers
Answer:
3.6069 × 104
Step-by-step explanation:
What would be the first step in solving this problem -18 = 2x
Answers
Can somebody explain why 8/17 is correct. Will make brainliest.
Answers
Answer:
8/17 is correct because cosine = adjacent/hypotenuse, and since angle A is theta, or the reference angle, the adjacent of A would be 8, and the hypotenuse is always across the right angle.
15/17 would be sine instead of cosine
Write the equation of the line in fully simplified slope-intercept form.
