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Chapter 10: Q2. (page 377)

Draw any AB炉.

a. Construct XY炉 so that XY=AB.

b. Using X and Y as centers, and a radius equal to AB, draw arcs that intersect. Label the point of intersection Z.

c. Draw XZ炉 and YZ炉.

d. What kind of triangle is 螖XYZ?

Short Answer

Expert verified

The triangle isequilateral.

Step by step solution

01

Step 1. Given information.

Two triangle is given, 螖ABC and 螖XYZ.

02

Step 2. Concept used.

Consider the line AB and draw the line XY炉such that XY=AB.

Consider the X and Y as centre and equal radius to draw an arc.

Consider the intersection point that is named Z and draw XZ炉and YZ炉

such that it form the triangle with all the sides are equal.

03

Step 3. Draw the figure.

In case all the sides are equal then the triangle is equilateral as shown in the Figure

Therefore, the triangle isequilateral as shown in the figure.

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Most popular questions from this chapter

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

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

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�.

1

Is there some kind of triangle such that the perpendicular bisector of each side is also an angle bisector, a median, and an altitude?

a.Draw any acute triangle. Bisect each of the three angles.

role="math" localid="1648851512702" b.Draw any obtuse triangle. Bisect each of the three angles

c.What do you notice about the points of intersection of the bisectors in parts a and b?

a
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