Given: GH || KL, J is the midpoint of HK Prove: AGHJ ALKJ
STATEMENT
REASON
1. GH | KL
Given
2. J is the midpoint of HK
Given
3
4
5
6.GHJ=LKJ

    Statements                              Reasons

1. GH║KL                                  1. Given

2. J is the midpoint of HK       2. Given

3. JH ≅ JK                                3. Definition of the midpoint of a segment

4. ∠JKL ≅ ∠JHG                      4. Alternate interior angles

5. ∠GJH ≅ ∠KJL                      5. Vertically opposite angles

6. ΔGHJ ≅ ΔLKJ                      6. By ASA theorem of congruence

We have to prove the statement, ∠GHJ = ∠LKJ

Given; GH || KL, J is the midpoint of HK.

To prove; ∠GHJ = ∠LKJ

Given; J is the midpoint of HK,

By definition midpoint of a segment,

The midpoint is the middle part of the line segment J, it is equidistant from both endpoints it is the centroid of the segment of the endpoints.

JH ≅ HK

Then, by the property of alternate interior angles,

∠JKL≅ ∠JKH

Therefore, by the property of vertically opposite angles,

When two lines intersect they form four angles. Vertical angles are the angles that are opposite to each other. Any two intersecting lines form two pairs of vertical angles that are opposite to each other.

∠GJH ≅ KJL

By ASA congruence theorem,

When two triangles are congruent to each other - If two angles and the involved side of one triangle is equivalent to the two angles and the included side of the other triangle.

ΔGHJ ≅ ΔLKJ

Hence Proved.

For more details refer to the link.

link

Step-by-step explanation:

From the picture attached,

Given:

GH║KL and J is the midpoint of HK.

To Prove:

ΔGHJ ≅ ΔLKJ

       Statements                              Reasons

1. GH║KL                                  1. Given

2. J is the midpoint of HK       2. Given

3. JH ≅ JK                                3. Definition of the midpoint of a segment

4. ∠JKL ≅ ∠JHG                      4. Alternate interior angles

5. ∠GJH ≅ ∠KJL                      5. Vertically opposite angles

6. ΔGHJ ≅ ΔLKJ                      6. By ASA theorem of congruence

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph