in triangle ABC,, AB=5cm, angle ABC=45°, BC=6cm and ON=5 CM. are the two triangles congruent? if yes,write the correspondence of its vertices.
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Class 7
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>>Constructions of Triangles
>>Draw a triangle ABC with BC...
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Draw a triangle ABC with BC=6cm, AB=5cm and ∠ABC =60
o
. Then construct a triangle whose sides are
4
3
of the corresponding sides of the Δ ABC.
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Solution
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The ΔA
′
BC
′
whose sides are
4
3
of the corresponding sides of ΔABC can be drawn as follows:
Step 1: Draw a ΔABC with side BC=6cm,AB=5cm,∠ABC=60
∘
Step 2: Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
Step 3: Locate 4 points, B
1
,B
2
,B
3
,B
4
on line segment BX.
Step 4: Join B
4
C and draw a line through B
3
, parallel to B
4
C intersecting BC at C
′
.
Step 5: Draw a line through C
′
parallel to AC intersecting AB at A
′
.
The triangle A
′
BC
′
is the required triangle.