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What are necessary when proving that the oppsite sides of a parallelogram are congruent check all that apply?
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Proving that a parallelogram has equal pair of sides?
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!
Have been proving?
This is present perfect continuous. They have been proving themselves very helpful.
Proving A hypothesis is called what?
'THEORY'
What does sas mean in geometery?
It is an acronym for the postulate "Side Angle Side". This is used to determine a triangle's congruency to other triangles. SAS is grouped often with SSS, AAS, and ASA (all "A"s are angle, all "S"s are side.)
What is the technique of indirectly proving something by showing that the alternative is absurd?
Apagoge
What is necessary when proving that the opposite sides of a parallelogram are congruent?
1. Opposite sides are parallel 2. Corresponding parts of congruent triangles are congruent
Are necessary when proving that the opposite angles of a parallelogram are congruent?
A basic knowledge of angles when two parallel lines meet a transversal is necessary.
What is necessary when proving that the opposite angles of a parallelogram are congruent?
Because its 4 interior angles must add up to 360 degrees
Is a rhombus always sometimes or never a parallelogram?
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.
What is necessary when proving that the diagonals of a rectangle are congruent?
opposite sides are congruent corresponding parts of congruent triangles are congruent(apex)
What are necessary when proving that the opposite sides of a parallelogram are congruent?
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
Why is drawing the diagonals of a parallelogram help full in proving many of the parallelograms properties?
It is helpful (not help full) because the two triangles formed by either diagonal are congruent.
What are necessary when proving that the diagonals of a rectangle are congruent?
A ruler or a compass would help or aternatively use Pythagoras' theorem to prove that the diagonals are of equal lengths
Proving that a parallelogram has equal pair of sides?
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!
How can proving two triangles congruent can help prove parts of the triangle congruent?
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
What method proves a trapezoid isosceles?
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.
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
