Curriculum

Course: Mathematics — Second Preparatory

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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Applications of Parallelism

Mathematics — Second Preparatory

Applications of Parallelism

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Two parallel lines are cut by a transversal. A corresponding angle is (3x + 10)° and the other corresponding angle is 100°. Find x	parallellinestransversalcorresponding
Solution	The angles are corresponding so they are equal: 3x + 10 = 100 so 3x = 90 and x = 30	anglescorrespondingequal
Example 2	Two parallel lines are cut by a transversal. The co-interior angles measure 2x° and 3x°. Find each angle	parallellinestransversalinterior
Solution	2x + 3x = 180 so 5x = 180 and x = 36. The angles are 72° and 108°. Check: 72 + 108 = 180	anglesCheck
Example 3	Two parallel lines are cut by a transversal. The alternate angles measure (x + 20)° and (2x − 50)°. Find the angle	parallellinestransversalalternate
Solution	The angles are alternate so they are equal: x + 20 = 2x − 50 so x = 70. The angle is 70 + 20 = 90°. Check: 2 × 70 − 50 = 90	anglesalternateequalangle

Comparison aspect	Main idea	Keywords
Example 4	Two parallel lines are cut by a transversal and one of the angles formed measures 65°. Find the measures of all eight angles	parallellinestransversalangles
Solution	Corresponding and alternate angles to the 65° angle are equal to it so they are 65°. The co-interior angles are supplementary to it so they are 180 − 65 = 115°. Vertically opposite angles are equal so the eight angles are four angles of 65° and four angles of 115°	Correspondingalternateanglesangle

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