# prove that consecutive angles of a parallelogram are supplementary

One of the properties of parallelograms is that the opposite angles are congruent, as we will now show. Then, look at the consecutive angles (or the ones that are next to each other). use the diagram and information to answer the question. Get Instant Solutions, 24x7. B. complementary. Since this a property of any parallelogram, it is also true of any special parallelogram like a rectangle, a square, or a rhombus,. given: ab∥cd m∠a = 104, m∠b = 76 prove: quadrilateral abcd is a parallelogram. A proof that in a parallelogram any pair of consecutive angles are supplementary by applying the consecutive interior angles theorem twice. you can prove that quadrilateral abcd is a parallelogram by showing that an angle of the quadrilateral is supplementary to both of its consecutive angles. In a parallelogram, opposite angles have equal lengths, and so in each parallelogram there are two pairs of equal angles. Consecutive Angles in a Parallelogram are Supplementary We might find that the information provided will indicate that the diagonals of the quadrilateral bisect each other. math. So, in a parallelogram you have two sets of parallel lines. Geometry answr. Since there are two pairs of angles and one of each pair is on each side, adjacent angles are supplementary (their sum makes 180˚) The following diagram explains: If so, then the figure is a parallelogram. Prove that the adjacent angles of a parallelogram are supplementary 2 See answers chyr1567 is waiting for your help. The consecutive angles of a parallelogram are. it follows that ad¯ is a transversal of parallel line segments ab¯ and cd¯, which makes ∠a and ∠d same-side interior angles along parallel line segments. A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. In a parallelogram, the angles add up to 360˚. Supplementary angles are two angles that add up to 180-degrees. The Consecutive Interior Angles Theorem states that the two interior angles formed by a transversal line intersecting two parallel lines are supplementary (i.e: they sum up … Consecutive angles are supplementary. Upvote (96) Was this answer helpful? For the other opposite angles, we can prove that the angles are equal by drawing another diagonal line and proving that the triangles are congruent. To prove this theorem take the generic parallelogram abcd. Take a look at one of the complementary-angle theorems and one of the supplementary-angle theorems in action: Before trying to write out a formal, two-column proof, it’s often a good idea to think through a seat-of-the-pants argument about why the prove statement has to be true. To help you remember. C. supplementary. If the shapes are supplementary, then the shape might be a parallelogram. Consecutive Angles Add UP to 180° Also, ∠B = ∠D, so the opposite angles are equal. Add your answer and earn points. In any case, in a parallelogram, the opposite angles are always equal. Problem Your are correct in that statement. Take one set, and one of other lines and continue it beyond that set of two lines. D. none of these. So are angles 3 and 5. Given: abcd is a parallelogram. Write a two-column proof of Theorem 6-2-3, which is: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Prove that the areas of triangles A B C and B Q P are equal. prove: any two consecutive angles of abcd are supplementary. Our experts are building a solution for this. write a two column proof for this Given:QR||TU , S is the midpoint of QT Prove: /\ QSR=~/\TSU /\ IS the triangle sign =~ is the congruent symbol . the quadrilateral abcd is a parallelogram, so by definition ab¯∥cd¯. Opposite angles are congruent consecutive angles are supplementary. The Theorem. Answer. Let’s say that two of the consecutive angles have measurements of 35-degrees and 145-degrees. A. equal. 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