Question

construct a triangle ABC in which BC=8cm angle B =45 degree and AB-AC=3.5cm

Answer 1

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Answer 2

The construction of ∆ABC is attached, having BC = 8 cm, AB-AC =3.5 cm and ∠B =45 °

Given:

• ∆ABC
• BC = 8 cm, AB-AC =3.5 cm
• ∠B =45°

To find:

• Construction of ∆ABC

Solution:

Steps of construction:

When AC<AB, the arc of difference of both sides is made above the base line.

1. Draw base side BC of 8 cm with the help of scale and pencil.
2. Draw 45° angle at point B with the help of protector/compass.
3. Mark an arc of AB-AC =3.5 cm on line of angle 45° in upward direction, mark that point D;as shown in figure.
4. Join D and C.
5. Made a perpendicular bisector of DC; Open the compass more than half of the length of DC and mark an arc in both sides of DC from both points i.e. D and C then join the midpoints of arc.
6. Perpendicular bisector of DC cuts angle 45° line, mark that point as A.
7. Join A to C.

Thus, construction of ∆ABC has done.

Verification:

On measurement

AC= 8 cm

AB= 11.5 cm

Thus,

AB-AC=11.5-8 =3.5 cm

Learn more:

1) Construct a triangle XYZ in which YZ=5 CM. XZ-XY=2.5 CM. angleY= 75°

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2) construct a triangle ABC in which AC=6.2 cm, ∠C=60° and AB-BC = 2.5 cm

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