Mathematics
Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ∠ABC. Find the point R on AD such that RB = RC. Measure the length of AR.
Answer
Draw AB = 4 cm as base of rhombus. From A cut an arc of 5 cm and from B cut an arc of 4 cm. Take their point of intersection as point C. From C cut an arc of 4 cm and from A also, take their point of intersection as point D. Join the points to form rhombus ABCD, and AC to form diagonal.
On measuring ∠ABC, it is equal to 78°.
We want to find a point R such that, RB = RC.
We know that locus of point equidistant from two points is the perpendicular bisector of the line segment joining them.
From figure,
PQ is the perpendicular bisector of BC and meets AD at point R, such that AR = 1.2 cm.
Hence, ∠ABC = 78° and AR = 1.2 cm.
Related Questions
By using ruler and compasses only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that
(i) P is equidistant from the sides BC and AC.
(ii) P is equidistant from the points B and C.
Without using set square or protractor, construct the quadrilateral ABCD in which ∠BAD = 45°, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.
(i) Measure ∠BCD.
(ii) Locate the point P on BD which is equidistant from BC and CD.
Without using set square or protractor construct :
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC.
Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point exist ?