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Constructions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct a $\triangle\text{ABC}$ in which BC = 8cm, $\angle\text{B}=45^\circ$ and $\angle\text{C}=60^\circ.$ Construct another triangle similar to $\triangle\text{ABC}$ such that its sides are $\frac35$ of the corresponding sides of $\triangle\text{ABC}.$
✓

Answer


Steps of Construction:
Step 1. Draw a line segment BC = 8cm.
Step 2. At B, draw $\angle\text{XBC}=45^\circ.$
Step 3. At C, draw $\angle\text{YCB}=60^\circ.$ Suppose BX and CY intersect at A.
Thus, $\triangle\text{ABC}$ is the required triangle.
Step 4. Below BC, draw an acute angle $\angle\text{ZBC}.$
Step 5.$\text { Along } B Z \text {, mark five points } Z_1, Z_2, Z_3, Z_4 \text { and } Z_5 \text { such that } B Z_1=Z_1 Z_2=Z_2 Z_3=Z_3 Z_4=Z_4 Z_5 \text {. }$
Step 6. Join $CZ_5$.
Step 7. From $Z_3$, draw $Z_3C' || CZ_5$ meeting BC at C'.
Step 8. From C', draw A'C' || AC meeting AB in A'.
Here, $\triangle\text{AB}'\text{C}'$ is the required triangle whose sides are $\frac{3}{5}$ of the corresponding sides of $\triangle\text{ABC}.$

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