मराठी

In Given Figure 1 Abcd is an Arrowhead. Ab = Ad and Bc = Cd. Prove Th at Ac Produced Bisects Bd at Right Angles at the Point M.

Advertisements
Advertisements

प्रश्न

In given figure 1 ABCD is an arrowhead. AB = AD and BC = CD. Prove th at AC produced bisects BD at right angles at the point M

आकृती
Advertisements

उत्तर

A is equidistant from B and 0 . Therefore, A lies on perpendicular bisector of BO. 

C is equidistant from Band 0. Therefore, C lies on perpendicular bisector of BO. 

A and C both lie on perpendicular bisector of BO. 

Hence, AC is perpendicular bisector of BO. 

Since AC is perpendicular bisector of BO so ∠ AMB = ∠ AMO = right angle.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Loci - Exercise 16.1

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Angle ABC = 60° and BA = BC = 8 cm. The mid-points of BA and BC are M and N respectively. Draw and describe the locus of a point which is:

  1. equidistant from BA and BC.
  2. 4 cm from M.
  3. 4 cm from N.
    Mark the point P, which is 4 cm from both M and N, and equidistant from BA and BC. Join MP and NP, and describe the figure BMPN.

Draw a straight line AB of 9 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement. 


Two straight roads AB and CD cross each other at Pat an angle of 75°  . X is a stone on the road AB, 800m from P towards B. BY taking an appropriate scale draw a figure to locate the position of a pole, which is equidistant from P and X, and is also equidistant from the roads. 


Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 


Construct a Δ XYZ in which XY= 4 cm, YZ = 5 cm and ∠ Y = 1200. Locate a point T such that ∠ YXT is a right angle and Tis equidistant from Y and Z. Measure TZ. 


In the given figure ABC is a triangle. CP bisects angle ACB and MN is perpendicular bisector of BC. MN cuts CP at Q. Prove Q is equidistant from B and C, and also that Q is equidistant from BC and AC. 


Using only ruler and compasses, construct a triangle ABC 1 with AB = 5 cm, BC = 3.5 cm and AC= 4 cm. Mark a point P, which is equidistant from AB, BC and also from Band C. Measure the length of PB. 


State and draw the locus of a point equidistant from two given parallel lines.


How will you find a point equidistant from three given points A, B, C which are not in the same straight line?


Without using set squares or protractor.
(i) Construct a ΔABC, given BC = 4 cm, angle B = 75° and CA = 6 cm.
(ii) Find the point P such that PB = PC and P is equidistant from the side BC and BA. Measure AP.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×