Leaving Cert Mathematics Proofs and Constructions: Question 6A

Prove that, if two

Question

Question 6A

Prove that, if two triangles $ABC$ and $A'B'C'$ are similar, then their sides are proportional, in order:

$$\frac{|AB|}{|A'B'|} = \frac{|BC|}{|B'C'|} = \frac{|CA|}{|C'A'|}$$

Given:
- The similar triangles $ABC$ and $A'B'C'$.

To Prove:
- $$\frac{|AB|}{|A'B'|} = \frac{|BC|}{|B'C'|} = \frac{|CA|}{|C'A'|}$$

Construction:
- Mark $B'$ on $AC$ such that $|AB'| = |A'B'|$.
- Mark $C'$ on $|AC|$ such that $|AC'| = |A'C'|$.

Diagram:

Proof:
- $\Delta ABC' \cong \Delta A'B'C'$ by SAS.
- Hence, $|B'C'| \parallel |BC|$ (by corresponding angles).
- Thus,

$$\frac{|AB|}{|A'B'|}, \frac{|BC|}{|B'C'|}, \frac{|CA|}{|C'A'|}$$ …Theorem.

(b) Given the line segment $\{BC\}$, construct, without using a protractor or set square, a point $A$ such that $|\angle ABC| = 60^\circ$. Show your construction lines.

Question 6A Prove that, if two triangles $ABC$ and $A'B'C'$ are similar, then their sides are proportional, in order: $$\frac{|AB|}{|A'B'|} = \frac{|BC|}{|B'C'|} = \frac{|CA|}{|C'A'|}$$ Given: - The similar triangles $ABC$ and $A'B'C'$ - Leaving Cert Mathematics - Question 6A - 2014

Given:

To Prove:

Construction:

Proof:

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