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.

The midpoint of the line is the point that divides in two halves of the same length.

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:

link

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

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.