In the diagram, \( \triangle ABC \) and \( \triangle DEF \) are drawn with \( \overline{A} = \overline{D}, \overline{B} = \overline{E} \) and \( \overline{C} = \overline{F} \) - NSC Mathematics - Question 11 - 2017 - Paper 2
Question 11
In the diagram, \( \triangle ABC \) and \( \triangle DEF \) are drawn with \( \overline{A} = \overline{D}, \overline{B} = \overline{E} \) and \( \overline{C} = \over... show full transcript
Worked Solution & Example Answer:In the diagram, \( \triangle ABC \) and \( \triangle DEF \) are drawn with \( \overline{A} = \overline{D}, \overline{B} = \overline{E} \) and \( \overline{C} = \overline{F} \) - NSC Mathematics - Question 11 - 2017 - Paper 2
Step 1
Construct points G and H
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Answer
On sides AB and AC of ( \triangle ABC ), mark points G and H such that ( AG = DE ) and ( AH = DF ). Draw line GH; mark point G on line AB and point H on line AC, ensuring that ( AG = DE ) and ( AH = DF ).
Step 2
Prove congruence of triangles
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Answer
To prove that ( \triangle AGH \cong \triangle DEF ), establish that:
( \angle AGH \equiv \angle DEF ) (given angles)
( AG = DE ) (constructed)
( AH = DF ) (constructed)
By the Angle-Side-Angle (ASA) postulate, ( \triangle AGH \cong \triangle DEF ).
Step 3
Establish relationships between sides
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Answer
From the congruence of triangles, we have:
( \frac{AG}{DE} = \frac{AH}{DF} )
This also leads to the proportional relationships:
( \frac{AC}{BC} = \frac{DE}{AB} )
Therefore, we conclude that ( \frac{DE}{AB} = \frac{AC}{BC} ) as required.
