Co Interior Angles
Co-Interior Angles
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Co-interior angles: The interior angles that lie between two lines and on the same side of a transversal are called co-interior angles. If the two lines are parallel, then co-interior angles add to give In the figure, the following pairs of angles are called pairs of consecutive interior angles: Theorem: If the transversal intersects two parallel lines, then each pair of co-interior angles are supplementary. Given: m and n are parallel lines and the transversal l cuts m and n To Prove : Proof: line m and l intersect each other therefore
Line m and n are parallel and the transversal l cuts them. From Eq. (1) and (2) Hence Proved that co-interior angles are supplementary. Theorem: If a transversal intersects two lines such that a pair of co-interior angles are supplementary, then the lines are parallel Given: m and n are lines and the transversal l cuts m and n and To Prove: m and n are parallel Proof: line m and l intersect each other therefore
and From Eq. (1) and (2) But they are alternate interior angles when the transversal l cuts the line m and n Since they are equal the lines are parallel. Hence Proved that the lines are parallel. Illustration: Identify co - interior angles from the given figure: Solution: <3 and <5 are co - interior <3 + <5 = 180. <4 and <6 are co - interior and <4 + <6 = 180. because AB and CD are two parallel lines and a transversal L intersects them: The converse of each of the above statements is also true. |
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Solution: As co-interior angles are supplementary 5x + 37 + 43 = 180 5x =180-80 5x=100 x = 20 |
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Given that the lines m and l parallel, then the angles shown in the image are:
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| Right Option : C | |||
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Find the value of
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| Right Option : C | |||
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Are the lines m and l parallel, then the angles shown in the image are:
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| Right Option : B | |||
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