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Opposite Angles Theorem Converse: If the opposite angles of a quadrilateral are congruent, then the figure is a parallelogram. Consecutive Angles Theorem Converse: If the consecutive angles of a quadrilateral are supplementary, then the figure is a parallelogram.
By Theorem, consecutive angles of a parallelogram are supplementary. So, we have. m∠A + m∠B = 180°. From the diagram, m∠A = 70°. 70° + m∠B = 180°.
Consecutive angles theorem states that if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. From the above figure, we can write. ∠3 + ∠5 = 180 o. ∠4 + ∠6 = 180 o.
What is the measure of m∠J ? 9 The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an obtuse angle of the parallelogram? 10 In parallelogram RSTU, m∠R = 5x − 2 and m∠S = 3x + 10. Determine and state the value of x.
Consecutive angles of a parallelogram are supplementary. Let us learn about these two special theorems of a parallelogram in detail. Theorem: In a parallelogram, the opposite angles are equal. Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively. To Prove: ∠A =∠C and ∠B=∠D.
Consecutive angles in a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. Methods might be used to prove that a quadrilateral is a parallelogram. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
The Consecutive Interior Angles Theorem (Theorem 3.4) states that if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
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