Use ruler and compass only for the following question- All construction lines and arcs must be clearly shown-Construct a ABC in which BC - 6-5 cm- - ABC - 60- AB - 5 cm- Construct a locus of points l1 at a distance of 3-5 cm from A- Also- construct a locus of points l2 which is equidistant from AC and BC- Let l1 intersect l2 in two points X and Y- Measure XY-

1. Draw base BC of length 6.5 cm . Make an angle of 60^∘ from B .2. Mark an arc of radius 5 cm from B on the 60^∘ angle ...

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Standard VII

Mathematics

Construction of a Triangle with SAS Criterion

Use ruler and...

Question

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
Construct a $△ A B C$ in which $B C = 6.5 c m, ∠ A B C = 60^{\circ}, A B = 5 c m$ . Construct a locus of points $l_{1}$ at a distance of $3.5 c m$ from $A$ . Also, construct a locus of points $l_{2}$ which is equidistant from $A C$ and $B C$ . Let $l_{1}$ intersect $l_{2}$ in two points $X$ and $Y$ . Measure $X Y$ .

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Solution

1. Draw base $B C$ of length $6.5 c m$ . Make an angle of $60^{\circ}$ from $B$ .
2. Mark an arc of radius $5 c m$ from $B$ on the $60^{\circ}$ angle created and name it as $A$ . Join $A - C$ . $△ A B C$ is the required triangle.
3. Draw a circle with centre as $A$ and radius $3.5 c m$ . This is the locus of the points equidistant from $A$ at a distance of $3.5 c m$ .
4. Draw the angle bisector of $∠ A C B$ which will be the locus of points equidistant from $A C$ and $B C$ ,
5. Measure the length of $X Y$ which comes out to be $5 c m$ .

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Similar questions

Use ruler and compass only for this question
(i) Construct $Δ A B C$ , where AB = 3.5 cm, BC = 6 cm and $∠ A B C = 60^{\circ}$
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C.

Then the length of PB is

Ruler and compasses may be used in this question.All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

(i) Construct a $△ A B C$ ,in which BC=6 cm,AB=9 cm and angle ABC= $60^{o}$ .

(ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C.

(iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.

(iv) Mark the point Q, in your construction.which would make $△ Q B C$ equal in are to $△ A B C$ , and isosceles.

(v) Measure and record the length of CQ.

Q. Construct a triangle

A B C

with

A B = 5.5 c m, A C = 6 c m

and

∠ B A X = 105^{o}

Hence :
Construct the locus of points equidistant from

B A

and

B C

Construct a triangle ABC, with AB=5.6 cm, AC=BC=9.2 cm.

Find the points equidistant from AB and AC; and also 2 cm from BC.

Measure the distance between the two points obtained.

Construct a $Δ$ ABC, in which BC = 6 cm, AB = 9 cm and $∠$ ABC = 60 $^{\circ}$

i. Construct the locus of all points inside $Δ$ ABC, which are equidistant from B and C.

ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC.

iii. Mark the point Q in your construction, which would make $Δ$ QBC equal in area to $Δ$ ABC, and isosceles.

iv. Measure and record the length of CQ.

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