Co-internal angles Co-interior angles, also known as consecutive interior angles or same-side interior angles, are pairs of angles that lie on the same side of a transversal and inside the two lines it intersects. These angles have specific properties depending on whether the lines they intersect are parallel or not. Definition and Identification (1) Transversal […]
Read More →Corresponding Angles – Definition – Examples Two angles that are corresponding are those that are located on the same side of a transversal in identical relative position. They typically result from a transversal cutting two lines, whether they are parallel or not. In other words corresponding angles formed when a transversal line cuts across two […]
Read More →Alternate Angles: Definition and Types In this tutorial we will learn definition and types of alternate angles. In geometry, alternate angles are a special kind of angles. Alternate interior angles are formed when a transversal intersect two parallel or non-parallel lines. If a straight line intersects two lines, in the same plane at two distinct […]
Read More →Alternate Interior Angles – Definition – Examples – Properties What are alternate interior angles? The term alternate interior angles is often used when two lines are intersected by a third line(transversal). Alternate interior angles are formed when two lines are intersected by a third line. The third line is known as the transversal line. Alternate […]
Read More →The sum of the angles of a triangle is 180º Given: A triangle △ PQR and ∠1, ∠2, and ∠3 are angles of triangle △ PQR. To prove: ∠1 + ∠2 + ∠3 = 1800 Construction: Draw a line XPY parallel to QR passing through P. Proof: XPY ∥ QR and PQ is transversal ∴ ∠2 = ∠4 (Alternate angles) ….(1) XPY ∥ QR and PR […]
Read More →Theorem : In a parallelogram, opposite angles are equal. Given: A parallelogram ABCD, opposite sides of parallelogram are side AB and side DC side AD and side BC. To prove: Opposite angles of parallelogram are equal. […]
Read More →Theorem – Alternate Interior Angles are Equal If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. Given: Two parallel Lines AB and CD, and PS be transversal intersecting AB at Q and CD at R. To Prove: Each pair of alternate interior angles are equal. i.e. ∠BQR = ∠CRQ and ∠AQR = ∠QRD […]
Read More →Exterior Angle of a Triangle If any side of a triangle is extended then the exterior angle of triangle is equal to the sum of its interior opposite angles. Given : A △ABC, side BC of △ABC is extended, ∠ACD is an exterior angle. To Prove : The sum of measure of exterior angle of triangle is equal to the sum […]
Read More →If a transversal intersect two parallel lines, then each pair of interior angles on the Same side of the transversal are Supplementary. Given: Two parallel Lines AB and CD, and PS be transversal intersecting AB at Q and CD at R. To Prove: Sum of interior angles on the Same side of the transversal is Supplementary. […]
Read More →If a transversal intersects two lines, such that a pair of alternate interior angles are equal then the two lines are parallel. Given: Two lines AB and CD, and PS be transversal intersecting, AB at Q and CD at R. Each pair of alternate interior angles are equal. i.e. ∠BQR = ∠CRQ and ∠AQR = ∠QRD To Prove: AB ∥ CD Proof: Transversal […]
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