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Standard VIII

Mathematics

Construct Triangle When Its Base, Difference of the Other Two Sides and One Base Angle Are Given

During the co...

Question

During the construction of a triangle given its base, a base angle and the sum of other two sides, which of the triangles formed are congruent?

△

ABC and

△

AMC

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△

ABC and

△

ADC

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△

ABC and

△

AMD

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△

AMC and

△

AMD

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Solution

The correct option is D $△$ AMC and $△$ AMD
Given,
Construction of a triangle given its base, a base angle and sum of other two sides.

If we take $△$ AMC and $△$ AMD,
DM = MC (perpendicular bisector bisects the line DC)
$∠$ AMC = $∠$ AMD = $90^{\circ}$ (perpendicular bisector)
AM = AM (common side)

$△$ AMC $≅$ $△$ AMD (By SAS Congruency)

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Similar questions

Q. In the given construction of triangle ABC in which the base BC, base angle ABC, and the difference of the sides AB and AC are given, line segment BD = ________ .

Q. Draw a ∆ABC in which base BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are

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To construct a triangle, given its base, a base angle and sum of other two sides, the first step is to draw the base side and one given angle.

How will you prove that the construction for a triangle with the given conditions is right?

Given conditions: Base length BC is given, base angle B is given, and difference of the other two sides is given (AB-AC) where AB is greater than AC. For going about the construction, I drew the base length BC, drew the ray BX with angle XBC known to me. Taking B as centre and radius equal to (AB-AC) I cut an arc on the ray BX intersecting it at point D. I then joined D to C. Then drew the perpendicular bisector of the line segment DC and named the point of intersection of this perpendicular bisector and the ray BX as A. Joined A to C and the triangle ABC was ready

Which of the following statements gives the best explanation to this construction?

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