ACT Preparation / Unit 13 ACT 1218 worked example, 60 to 90 seconds
Using Quadrilateral Properties
The idea
Quadrilateral problems are solved in three steps. First, identify the figure from what is given: parallel sides, equal sides, right angles. Second, list the properties that figure guarantees: equal opposite sides or angles, supplementary consecutive angles, and bisecting, equal or perpendicular diagonals. Third, write an equation from the property that connects the given and the unknown.
In practice
Worked example: in parallelogram ABCD, angle A is 2x + 15 and angle B is 3x − 10. Consecutive angles are supplementary, so 5x + 5 = 180, x = 35, angle A = 85° and angle B = 95°. Second: in rectangle PQRS, diagonal PR is 3x + 4 and diagonal QS is 5x − 8. A rectangle's diagonals are equal, so 3x + 4 = 5x − 8, x = 6, and each diagonal is 22.
Where people slip
Use only the properties the figure is known to have. A parallelogram's diagonals bisect each other, but assuming they are perpendicular treats it as a rhombus.
Your place on the trail
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Unlocks
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