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
|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°
To construct the quadrilateral PQRS, follow these steps:
Step 1: Draw a straight line PQ of length 8 cm.
Step 2: At point Q, draw an angle of 105 degrees, using a protractor. This will give you the line QR.
Step 3: Measure a line segment PR of length 9 cm, starting from point P. Draw this line.
Step 4: From point R, draw a line segment RS of length 9 cm, parallel to QR. This means that RS will be a straight line connecting to the endpoint of PQ.
Step 5: Draw a line segment RQ to complete the quadrilateral PQRS. RQ should be equal in length to RS, making the opposite sides equal.
Now, let's find the measurements you asked for:
To measure angle RSL:
Use a protractor to measure the angle between line segments RS and RL.
To measure length PS:
Measure the distance between points P and S using a ruler.
To measure angle QRS:
Use a protractor to measure the angle between line segments QR and RS.
To construct the quadrilateral PQRS, follow these steps:
1. Draw a line segment of length 9 cm and mark the endpoints as point P and point R.
2. At point P, draw a line segment of length 8 cm at an angle of 105° with PR. Mark the endpoint as point Q.
3. At point Q, draw a line segment of length 9 cm that intersects line segment PR. Mark the intersection point as point S.
Now, let's find the measures you're asking for:
1. Measure /RSL/:
Since line segment RS and line segment RQ have the same length (9 cm) and line segment RQ is perpendicular to line segment PQ, then angle RSL will be a right angle (90°).
2. Measure /PS/:
To find the measure of line segment PS, you can simply measure the length of the line between points P and S directly using a ruler.
3. Measure <QRS:
To find the measure of angle QRS, use a protractor to measure the angle between line segment QR and line segment RS at point R. That will give you the measure of angle QRS.