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Q: What are necessary when proving that the oppsite sides of a parallelogram are congruent check all that apply?

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First draw a parallelogram. I cannot draw one here so I will have to describe the picture and you should draw it. Let ABCD be a parallelogram. I put A on the bottom left, then B on the bottom right, C on the top right and D on the top left. Of course the arguments must apply to an arbitrary parallelogram, but just so you can follow the proof, that is my drawing. Now draw a segment from A to C. It is a diagonal. AB is parallel to CD and AD is parallel to BD because a parallelogram is a quadrilateral with both pair of opposite sides parallel. Now ABC and CDA both form triangles. Let angles 1 and 4 be the angles created by the diagonal and angle BCD of the parallelogram. Angle 1 is above and angle 4 is below. Similarly, let angles 3 and 2 be created by the intersection of the diagonal and angle DAB or the original parallelogram. Now angles 1 and 2 are congruent as are 3 and 4 because if two parallel lines are cut by a transversal, the alternate interior angles are congruent. Next using the reflexive property AC is congruent to itself. Now triangle ABC is congruent to triangle CDA by Angle Side Angle (SAS). This means that AB is congruent to CD and BC is congruent to AD by corresponding parts of congruent triangles are congruent (CPCTC). So we are done!

This is present perfect continuous. They have been proving themselves very helpful.

'THEORY'

In geometry, SAS stands for "side-angle-side," which refers to a method of proving congruence between two triangles. It states that if two sides and the included angle of one triangle are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent.

Proving the Riemann conjecture.

Related questions

1. Opposite sides are parallel 2. Corresponding parts of congruent triangles are congruent

A basic knowledge of angles when two parallel lines meet a transversal is necessary.

Because its 4 interior angles must add up to 360 degrees

Always. In fact, one method of proving a quadrilateral a rhombus is by first proving it a parallelogram, and then proving two consecutive sides congruent, diagonals bisecting verticies, etc.

opposite sides are congruent corresponding parts of congruent triangles are congruent(apex)

A. Corresponding parts of similar triangles are similar.B. Alternate interior angles are supplementary.C. Alternate interior angles are congruent.D. Corresponding parts of congruent triangles are congruent

It is helpful (not help full) because the two triangles formed by either diagonal are congruent.

A ruler or a compass would help or aternatively use Pythagoras' theorem to prove that the diagonals are of equal lengths

First draw a parallelogram. I cannot draw one here so I will have to describe the picture and you should draw it. Let ABCD be a parallelogram. I put A on the bottom left, then B on the bottom right, C on the top right and D on the top left. Of course the arguments must apply to an arbitrary parallelogram, but just so you can follow the proof, that is my drawing. Now draw a segment from A to C. It is a diagonal. AB is parallel to CD and AD is parallel to BD because a parallelogram is a quadrilateral with both pair of opposite sides parallel. Now ABC and CDA both form triangles. Let angles 1 and 4 be the angles created by the diagonal and angle BCD of the parallelogram. Angle 1 is above and angle 4 is below. Similarly, let angles 3 and 2 be created by the intersection of the diagonal and angle DAB or the original parallelogram. Now angles 1 and 2 are congruent as are 3 and 4 because if two parallel lines are cut by a transversal, the alternate interior angles are congruent. Next using the reflexive property AC is congruent to itself. Now triangle ABC is congruent to triangle CDA by Angle Side Angle (SAS). This means that AB is congruent to CD and BC is congruent to AD by corresponding parts of congruent triangles are congruent (CPCTC). So we are done!

When you prove a triangle is congruent to another, it can help you prove parts of the triangle congruent by checking the ratio between all sides and angles. Thank you for asking

A trapezoid can be proven isosceles by proving that the 2 legs are congruent (by definition), or that the 2 base angles (either upper or lower) are congruent.

Given two sets of angles and the included side congruent, we seek a sequence of rigid motions that will map Δ_____onto Δ___ proving the triangles congruent.