Question
Construct a quadrilateral pqrs such that /pql=8cm,qps =105,angle pqs=30°,/pr/=9cm,/rs/=9cm,/RS/=/rq/
Measure /rsl
measure/ps/
Measure<qrs
Measure /rsl
measure/ps/
Measure<qrs
Answers
oobleck
|RS| = |RQ| = 9
Since |PR| = 9, ∆PRQ is isosceles, with ∡QPR = 30° and ∡QRP = 120°,
making ∡RQS = 75°
Then ∆PSR is isosceles, so ∡PSR = 75° and ∡PSR = 30°
That makes ∡QRS = 150°
|PS| = 2 * 9 sin15°
Since |PR| = 9, ∆PRQ is isosceles, with ∡QPR = 30° and ∡QRP = 120°,
making ∡RQS = 75°
Then ∆PSR is isosceles, so ∡PSR = 75° and ∡PSR = 30°
That makes ∡QRS = 150°
|PS| = 2 * 9 sin15°