   Chapter 1.4, Problem 40E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 33 to 40, use only a compass and a straightedge to perform the indicated constructions. Given: Straight ∠ A B C and B D → Construct: Bisectors of ∠ A B D and ∠ D B C What type of angle is formed by the bisectors of the two angles? To determine

To construct:

The bisector of given angles.

Explanation

Given:

The given angles are,

ABD and DBC

The Straight ABC and BD is given.

The given figure is,

Figure (1)

Approach:

Use compass to make an arc that intersect sides of ABD at point G and H as shown in figure (2).

Figure (2)

With G and H as centre mark two arcs equal radii to intersect at an interior point S of ABD then draw a ray from BS as shown in figure (3).

Figure (3)

Repeat the above procedure to obtain the bisector of DBC.

The required bisector of DBC is shown in figure (4).

Figure (4)

The bisector divided the given angle into two equal parts.

BS divide ABD into two equal parts. This gives,

mABS=mDBS

BT divide DBC into two equal parts. This gives,

mDBT=mCBT

All the angles lies on the straight line, it means the sum of all the angles is 180°

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