In parallelogram ABCD, E is the midpoint of AB and F is the midpoint of DC . Let G be the intersection of the diagonal DB and the line segment EF . Prove that G is the midpoint of EF.
Answers
The midpoint of the line is the point that divides
in two halves of the same length.
- ΔDFG ≅ ΔBGE and
≅
by CPCTC, therefore, Gis the midpoint of
Reasons:
The given parameters are;
The midpoint of AB in parallelogram ABCD = E
The midpoint of DC = F
Point of intersection of EF and DB = Point G
Required:
To prove that point G is the midpoint of EF.
Solution:
Statement Reason
1. m∠BDC ≅ m∠ABD 1. Alternate angles theorem
2. m∠DGF ≅ m∠BGE 2.Vertical angles theorem
3. =
3. Opposite sides of a parallelogram ABCD
4. ≅
4. Definition of midpoint of DC
5. =
5. Definition of congruency
6. +
= DC
6. Segment addition property
7. +
= DC
7. Substitution property
8. 2· = DC
8. Addition
9. = 0.5·
=
9. Division property
Similarly;
10. = 0.5·
=
10. Division property
11. 0.5· = 0.5·
11. Multiplication property of equality
12. =
12. Substitution property
13. ΔDFG ≅ ΔBGE 13. Angle-Angle-Side rule of congruency
14. ≅
14. CPCTC
15. =
15. Definition of congruency
16. Point G is the midpoint of 17. Definition of midpoint
Learn more about the midpoint of a line here:
Answer:
GF = GE that prove G is the mid-point of EF
Step-by-step explanation:
In the Parallelogram ABCD
∵E is the mid-point of AB
∵F is the mid-point of CD
∵AB = CD opposite sides in the parallelogram
∴EB = DF⇒(1)
∵AB // CD opposite sides in the parallelogram
∴m∠EBD = m∠FDB alternate angles ⇒(2)
∵BD intersects EF at G
∴m∠BGE = m∠DGF vertically opposite angles ⇒(3)
By using (1) , (2) and (3) you can prove:
ΔBGE is congruent to ΔDGF ⇒ AAS
∴GF = GE
∴G is the mid-point of EF
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Which statement about the given equation is NOT true?3x + 4y = 12 a. It is in slope-intercept form with a positive slope of 4/3. b. It is an example of a linear equation. c. It has two variables and has coefficients of 3 and 4. d. It represents a line which, when graphed, doesn't pass through the origin.
Add the polynomials (7x3−2x2−12)+(−3x3−8x2+10x)
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Answers
Answer:
Step-by-step explanation:
C (106)
g(x)=f(x)*h(x) ⇒g'(x)=f'(x)*h(x)+f(x)*h'(x) ⇒ g'(3)=f'(3)*h(3)+f(3)*h'(3)⇒ g'(3)=(8*2)+(6*15)= 16+90=106
Answers
The total pages in the book are 46.
What is equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Rosa read 10 pages of a book on Monday. She read 1/3 of the remainder on Tuesday, and she still had 24 pages to read,
Let the total number of pages be x,
Establishing the equation, we get,
10+(x-10) / 3+24 = x
30 + x - 10 + 72 = 3x
92 = 2x
x = 46
Hence, The total pages in the book are 46.
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Answer:
There are 46 pages in the book.
Step-by-step explanation:
if she already read 10 pages of the book and the remainder is split into 3rds and she already read 1/3 of the book then the 24 pages get divided by the 2/3 left which equals 12 so each third is 12 pages so 12 x 3 = 36 + 10= 46
There are 46 pages in the book.
A:4/5
B:-2
C:4
D:5
Answers
The 4/5 is the constant of proportionality/unit rate for the proportional relationship.
We have given that,
the unit rate for the proportional relationship is represented by the equation y=4/5x.
We have to determine the unit rate
What is the equation of proportionality?
The equation for proportionality is y = kx, where k is the constant of proportionality.
So in y = 4/5x,
The 4/5 is the constant of proportionality/unit rate for the proportional relationship.
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Answer:
A: 4/5
Step-by-step explanation:
The equation for proportionality is y = kx, where k is the constant of proportionality. That is what you're looking for in this question.
So in y = 4/5x, 4/5 is the constant of proportionality/unit rate for the proportional relationship.
Answers
Answers
Answer:
the correct answer is B.
Step-by-step explanation:
and can u get me 5 stars please and thank u
Answers
(we don't take care of lest powers , only the upper power)
Answer C