100 ! brainliest

write a proof to show that opposite angles of a parallelogram are congruent. be sure to create and name the appropriate geometric figures. this figure does not need to be submitted

Step-by-step proof:

Check the attached picture

Statement - Reason

Parallelogram ABCD - Given

Line AC - two points determine a line

AB║CD ; AD║BC - A parallelogram has 2 pairs of opposite sides parallel

∠1 ≅ ∠4 ; ∠2 ≅ ∠3 - line AC acts as a transversal for the parallel sides therefore, they are congruent through alternate interior angles

Line AC ≅ Line AC - Reflexive property

ΔABC ≅ ΔCDA - ASA (Angle - Side - Angle postulate)

∠D = ∠B - CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

m∠1 = m∠4 ; m∠2 = m∠3 - Congruent angles have congruent measures

m∠1 + m∠2 = m∠3 + m∠4 - Addition property of equality

m∠1 + m∠2 = m∠DAB                                                                                        m∠3 + m∠4 = m∠BCD - Angle Addition Postulate

m∠DAB = m∠BCD - Substitution

∠DAB = ∠BCD - Congruent angles have equal measures.

Hope this helps :)

See below.

Step-by-step explanation:

The opposite sides of a parallelogram are parallel ( The definition of a parallelogram).

If the Parallelogram is ABCD then

m < A + m < B = 180 degrees ( 2 inside angles of the parallel lines AB and DC.

Similarly :

m < C + m < B = 180   ( The sides AD and BC are parallel).

Subtracting the 2 above equations:

m < A -  m < C = 0

So we have proved that

 < A is congruent to < C - which are opposite angles.

In the same way we can prove that the other 2 opposite angles B and D are also congruent.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: