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Chapter 10: Q27. (page 385)

Draw three noncollinear points R,S,and T. Construct a triangle whose sides have R,S,and T as midpoints.

Short Answer

Expert verified

The figure is,

Step by step solution

01

Step 1. Given information.

Three noncollinear pointsR,S,and Tare given.

02

Step 2. Follow the ways.

Consider the following ways-

Draw a line joining RandT, since Rand Tare the mid points of two sides, RT炉is parallel to the third side for which Sis the midpoint.

Construct a line parallel to RT炉on point S,

by constructing 鈭�1=鈭�TRS.

Since RT炉is half of the third side, open the compass and measures the line RT炉.

Put the compass needle on Sand cut both sides at points Band C.

Join the points Band C.

Join the points Band R, and extend the line such that Ris the midpoint of AB炉.

Similarly join the points Cand T, and extend the line such that Tis the midpoint of AC炉.

03

Step 3. Construct the figure.

Therefore, the required figure drawn above.

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Most popular questions from this chapter

Construct a six-pointed star using the following procedure.

1. Draw a ray, AB鈫�. On AB鈫� mark off, in order, points C and D such that AB=BC=CD.

2. Construct equilateral 螖ADG.

3. On AG炉 mark off points Eand F so that both AEand EF equal AB.

4. On GD炉 mark off points Hand I so that both GHand HI equal AB.

5.To complete the star, draw the three lines FH鈫�,EB鈫�,and CI鈫�.

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Draw, if possible, a triangle in which the perpendicular bisectors of the sides intersect in a point with the location described.

  1. A point inside the triangle
  2. A point outside the triangle
  3. A point on the triangle

A parallelogram with perpendicular diagonals is a ____.

Draw a diagram roughly like the one shown. Without laying your straightedge across any part of the lake, construct more of RS鈫�.

Draw a segment and let its length be 1.

a. Construct a segment of length 5.

b. Construct a segment of length 12+52, or 1+52.

c. Construct a golden rectangle whose sides are in the ratio 1:1+52.

a
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