Question

100 POINTS!!!!! BRAINLIEST

Answer 1

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 :)

Answer 2

Answer:

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.