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Q19E

Expert-verifiedFound in: Page 470

Book edition
3rd

Author(s)
Thomas W Hungerford, David Leep

Pages
608 pages

ISBN
9781111569624

**Let ${\mathit{A}}$ be a constructible point not on the constructible line${\mathit{L}}$** **. Prove that the line through ${\mathit{A}}$ parallel to ** ${\mathit{L}}$**is constructible.**** [Hint: Use Exercise ** ${\mathbf{17}}$** to find a constructible line M through ${\mathit{A}}$ , perpendicular to ** ${\mathit{L}}$**. Then construct a line through ${\mathit{A}}$ perpendicular to$\mathit{M}$ ** **.]**

The line through $\text{A}$ parallel to $L$ is constructible.

**Drawing precise lines, line segments, shapes, circles, and other figures with a ruler, compass, or protractor is known as geometric construction.**

Consider that If $\text{C}$ is constructible point and $L$ is constructible line , then line perpendicular to $L$ and passing through$\text{C}$ is constructible.

The line $L$ is constructible, then the point$A$ is also constructible but not on line$L$ . From the step 1^{st} ,a line perpendicular to$L$ and passing through$A$ is constructible, say $N$ .

Similarly, draw a line perpendicular to $N$and passing through $\text{AO}$ , say $O$.

The line $O$ is perpendicular to $N$ which is perpendicular to$L$ . Hence, $O$is perpendicular to $L$ and also passes through $A$.

Hence, the line through $A$parallel to $L$ is constructible.

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