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What is the proof of The consecutive angles of a parallelogram are supplementary?
Wiki User
∙ 13y ago
So, in a parallelogram you have two sets of parallel lines. Take one set, and one of other lines and continue it beyond that set of two lines. Now, the single line is known as a tranversal, and by the same-side interior angles therom, the consecutive angles you are talking about must be congruent. The argument is the same on the opposite side. This is a lot easier with a diagram, ask your math teacher sometime.
Wiki User
∙ 13y ago
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Does an irregular hexagons interior angles equal 720?
Yes. All hexagons have interior angles totalling 720 degrees, whether they are regular or irregular. The proof of this is fairly easy.
The sum of 3 consecutive odd numbers is 59 what are the numbers?
The sum of three consecutive odd numbers must be divisible by 3. As 59 is not wholly divisible by 3 the question is invalid. PROOF : Let the numbers be n - 2, n and n + 2. Then the sum is 3n which is divisible by 3. If the question refers to three consecutive numbers then a similar proof shows that the sum of these three numbers is also divisible by 3. Again, the question would be invalid.
Three consecutive numbers that add up to a multiple of three?
EVERY three consecutive numbers add to a multiple of 3: Proof: numbers are n, n + 1 and n + 2. The total is 3n + 3 or 3(n + 1) This means that for any three consecutive numbers, the total is 3 times the middle number.
Prove that the bisectors of the angles of a linear pair are at right angle?
I am working on the same exact proof right now and i am lost
What is the proof that the sum of the angles of a hexagon equals 720?
There are 6 angles in a hexagon, and each angle measures 120 degrees. 120 x 6, or 120+120+120+120+120+120=720.
Can you write a two column proof given angles 2 and 3 are congruent and prove angles 1 and 4 are congruent?
Without a visual or more information, I'm guessing that the picture is of angles 1 and 2 that are consecutive (share an angle side) and a separate picture of consecutive angles 3 and 4. With that said: 1) angle 2 congruent to angle 3................1) given 2) angle 1 is supplementary to angle 2....2) If angles are next to each other --> supps angle 3 is supplementary to angle 4 3) angle 1 congruent angle 4..............3) If supps to congruents angles ---> congruent
what-Helena was asked to prove that any pair of vertical angles is congruent. She was provided a diagram with several pairs of vertical angles.?
A+
which completes the paragraph proof below?
supplementary
Do a parallelograms diagonals bisect each other?
I can't offer a full proof, but I can suggest some possibilities that will lead you to your proof. In a parallelogram, you can easily demonstrate that the angles formed by a cord extending between parallel lines and the parallel lines themselves, and that are formed on opposite sides of the cord, are equal. This will work for both pairs of triangles in the parallelogram, and can be applied to all of the angles at the corners of the parallelogram. This will lead you to demonstrating that the pairs of triangles "pointing" to each other (not adjacent pairs) are similar, and in fact congruent. From there it is not difficult to establish that the connected sections of the two interior cords are equal.
which is the reason for statement 4 in the proof?
corresponding angles
What is Proposition 1.8 of Metrica?
Proposition 1.8 of Metrica states that if the sum of the measures of two angles is less than 180 degrees, then the two angles are not supplementary. In other words, if the sum of two angles is less than a straight angle, then they are not a pair of supplementary angles.
How do you do proof of congruence?
Congruent shapes are identical in size and angles
Proof of parallelogram law of forces?
The parallelogram law states that when two concurrent forces F1 &F2 acting on a body are represented by two adjacent sides of a parallelogram the diagonal passing through their point of concurrency represents the resultant force R in magnitude and direction
which statement is missing from the following proof theorem: vertical angles are congruent.?
A+
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!
When writing a geometric proof which angle relationship could be used alone to justify that two angles are congruent?
Vertical angles
What is a two-column proof?
2 Column Proof: If a transversal intersects two parellel lines, then alternate interior angles are congruent.
