Construction of a triangle given a base and base angle and the difference of other two sides
Construction of a triangle given a base and base angle and the difference of other two sides
Construction of a triangle given a base and base angle and the difference of other two sides : In order to contruct a triangle when its base, difference of the other two sides and one of the base angles are given, we follow the following steps:
Steps of Contruction: Obtain the base, base angle and the difference of two other sides. Let BC be the base, be the base angle and x be the difference of the other two sides AB and AC of
.. There can be two cases
Case I: AB > AC i.e., x =AB - AC
STEP I Draw the base BC of given length. STEP II Draw STEP III AS AB > AC , then cut off segment BD = AB - AC from ray BX STEP IV . Join DC |  |
| STEP V: From point C taking radius more than half of CD Draw arc on both side of CD. |  |
| STEP VI : From point D taking same radius as in step V Draw arc on both side of CD to intersect the arcs drawn in step V at point P and Q. |  |
| STEP VII : Join PQ . This is the perpendicular bisector of CD meeting BX at A. |  |
| STEP VIII Join AC to obtain the required triangle ABC. |  |
Case II: AC > AB i.e., x =AC - AB
STEP I Draw the base BC of given length. STEP II Draw STEP III As AC > AB ,extend XB to D such that BD = AC - AB STEP IV . Join DC |  |
| STEP V: From point C taking radius more than half of CD Draw arc on both side of CD. |  |
| STEP VI : From point D taking same radius as in step V Draw arc on both side of CD to intersect the arcs drawn in step V at point P and Q. |  |
| STEP VII : Join PQ . This is the perpendicular bisector of CD meeting BX at A. |  |
| STEP VIII Join AC to obtain the required triangle ABC. |  |
Justification: Let us now see how do we get the required triangle. Since A lies on the perpendicular bisector of DC.
AD = AC
So, BD = AD - AB = AC - AB
Example : Construct a triangle ABC in which base AB = 5 cm, and AC - BC = 2.5 cm.
SOLUTION In order to construct the triangle ABC, we follow the following steps:
Steps of Construction:
STEP I Draw base AB = 5 cm
STEP II Draw
STEP III From ray AX, cut off line segment AD = 2.5 cm(=AC-BC)
STEP IV Join BD.
STEP V Draw the perpendicular bisector of BD which cuts AX at C.
STEP VI Join BC to obtain the required triangle ABC.
Justification: Since C lies on the perpendicular bisector of DB. THerefore,
CD = CB
Now, AD = 2.5 cm
AC - CD = 2.5 cm
AC - BC = 2.5 cm
Hence, is the required triangle.
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