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What is necessary when proving that the opposite angles of a parallelogram are congruent?
Wiki User
∙ 9y ago
Because its 4 interior angles must add up to 360 degrees
Wiki User
∙ 9y ago
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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 postulate or theorem verifies the congruence of triangles?
sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.
How you can prove that two triangles are congruent?
In order for 2 triangles to be congruent, it must be true that each pair of corresponding sides are congruent (equal in length) and each pair of corresponding angles are congruent (equal in size). It is not necessary to prove that all three pairs of sides and all three pairs of angles are congruent. If you prove that all the sides are congruent, then the angles must be congruent, too. This is known as SSS, the side-side-side method of proving congruency. There a four basic ways to prove congruency. They are: 1. SSS (side-side-side) Prove that all three pairs of sides are equal in length. 2. SAS (side-angle-side) Prove that two sides and the angle between them are equal. 3. ASA (angle-side-angle) Prove that two angles and the side between them are equal. 4. AAS (angle-angle-side) Prove that two angles and a side that is NOT between them are equal. Note that you cannot prove that triangles are congruent with AAA or SSA. Note: for right triangles we can use HL. This is a special method that just looks at the hypotenuse and the leg of one triangle and compares it to the hypotenuse of the other. However, if they are both right triangle, the angle between the hypotenuse and the leg is a right angle so this is really just a special case of AAS that we can only use for right triangles.
What are the 5 shortcuts used for proving triangles are congruent?
I only know 3. SSS (side/side/side) -> if all three sides are the same length SAS (side/angle/side) -> if two sides and the angle between them are the same ASA (angle/side/angle) -> if two angles and the side between them are the same
Are all squares similar true or false?
True. If all sides are congruent, and each angle is 90 degrees(keep in mind that in a four sided polygon, it adds up to 360), then the polygon is a square. All the square's sides will be proportional to each of the other squares sides, which makes it similar. For example, if one square has a side length of 2, and another has a side length of 4, then the proportion would be 2\4, or 1\2. Since each side is congruent, then each side would be proportional. If you are proving, the squares diagonal, then the square, then it would be still proportional. Remember it would be a 45-45-90 triangle, with two angle bisected, and one left alone. 45-45-90 triangles are equal to the proportion x-x-x \/(2) (square root of two). So 2\/2 would be proportional to 4\/4 proving that any combo in a square would make it similar. I hope this helps :D -AnonymousSaber
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 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
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.
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!
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.
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.
What does it mean to prove that two figures are congruent using rigid motions?
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.
