alternate interior angles are congruent in parallelogram?
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Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles. Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. ... You can show that alternate interior angles are congruent and hence lines are parallel for this part of the proof.
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1 Answer. We know that consecutive interior angles of a parallelogram are supplementary. Thus, two consecutive angles are (30 + 60)° , (2 × 30 + 30)° i.e. 90° and 90°. Hence , the special name of the given parallelogram is ractangle.
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ANSWER: Show that a pair of corresponding angles is congruent, show that a pair of alternate interior angles is congruent, show that a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary.
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['The opposite angles of a parallelogram are equal.', 'The opposite sides of a parallelogram are equal.', 'The diagonals of a parallelogram bisect each other.']
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When the two lines intersected by the transversal are parallel, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles become supplementary, which means they have a sum of 180 degrees.
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The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .
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Prove that opposite sides of a parallelogram are congruent. ... By the same token, segment AB is parallel to segment DC according to the definition of a parallelogram. Line AC is a transversal for segment BC and segment AD. This transversal creates alternate interior angles 1 and 4 which are equal as shown below.
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The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.
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The diagonals of a parallelogram are not equal. ... Because the parallelogram has adjacent angles as acute and obtuse, the diagonals split the figure into 2 pairs of congruent triangles. Since the angles are acute or obtuse, two of the shorter sides of the triangles, both acute and obtuse are congruent.
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Alternate Interior Angle Theorem The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .
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All sides and angles are congruent. Opposite sides are parallel to each other. The diagonals are congruent. The diagonals are perpendicular to and bisect each other.
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The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 .
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Consecutive angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. The four angles of a rhombus are right angles.
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Which property is not true for all parallelograms? (1) Opposite angles are congruent. (2) Opposite sides are congruent. (3) Consecutive angles are supplementary.
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Identify each parallelogram as a rectangle, rhombus, or a square. Answer: ... In Parallelogram B, we see that there are four right angles and that the pairs of opposite sides are congruent. However, consecutive sides are not congruent, so we can eliminate rhombuses and squares from our options.
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A parallelogram is a quadrilateral with both pairs of opposite sides parallel. ... THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite sides congruent. * THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent.
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Parallelograms: The Two Pairs of Opposite Angles are Congruent. A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. One of the properties of parallelograms is that the opposite angles are congruent, as we will now show.