Construction of a Triangle ABC with Given Base, Base Angle and Difference between Two Sides AB & AC, with AB >AC
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Q. Pavan asked Preeti to draw a triangle. He gave following data
1. the base BC
2. a base angle, say ∠B
3. The difference of other two sides AB – AC or AC – AB, Assume, AB > AC
She was unable to draw the triangle ABC. So as a hint he gave steps of construction but it was not in correct order. He gave following steps
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Join DC and draw the perpendicular bisector, say PQ of DC.
3. Cut the line segment BD equal to AB – AC from ray BX.
4. Let it intersect BX at a point A. Join AC
Arrange the steps in correct order.
1. the base BC
2. a base angle, say ∠B
3. The difference of other two sides AB – AC or AC – AB, Assume, AB > AC
She was unable to draw the triangle ABC. So as a hint he gave steps of construction but it was not in correct order. He gave following steps
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Join DC and draw the perpendicular bisector, say PQ of DC.
3. Cut the line segment BD equal to AB – AC from ray BX.
4. Let it intersect BX at a point A. Join AC
Arrange the steps in correct order.
- 1, 2, 3, 4
- 1, 4, 3, 2
- 1, 4, 2, 3
- 1, 3, 2, 4
Q.
For constructing a triangle with a given base, a base angle and difference between the other two sides, a
Q.
Which of the following congruencies could be the test for the construction of triangles where there is base length given, one of the base angles is given and the difference between the other two sides of the triangle are given?
RHS Congruency
ASA Congruency
SSS Congruency
None of these
