Question

Suppose P is a point on the line l. Justify the following construction for the line perpen- dicular to l through P. 1 • Pick a point O not on l and draw the circle with center 0 and radius OP. Let Q be the second point of intersection of this circle with l. • Draw the line (QO) and let R be the second point of intersection of this line with the circle. • Draw the line (RP). Perform this construction in GeoGebra and verify that l I (RP) by measuring the corre- sponding angle. Prove that l I (RP). Hint: Let M be the midpoint of PQ, prove that AOQM RQP.

Modern Geometry

Answer 1

X e 8 Here (a) is the we have to center of the circle. poove Rp te [RPa = 90o . let -roal Orl=8 radius of crolle. we know sides of equal lengths have same opposite angles in a triangle in trinagle kop, (RO) a lop] Now we kow In triangle lop) 5 от 3 LOOP= sum of all three internal angles of a triangle is 180° 3PRQ & miRp8 POR sho & @1 + O2) 2 ColtO2) = 180° ditor = qu m RpQ = RP Il (Proved) + O2 =180°