Triangle $ABC$ is a right-angled triangle with angle $ACB = 90^\circ$. $ADEB$, $BCGF$ and \(

Question

Triangle $ABC$ is a right-angled triangle with angle $ACB = 90^\circ$. $ADEB$, $BCGF$ and $ACHI$ are squares. $CJK$ is a straight line such that $CJK$ is perpendicular to $AB$ and $DE$. Show that triangles $DAC$ and $BAI$ are congruent, hence the area of quadrilateral $ADKJ$ and the area of square $ACHI$ are equal; triangles $BEC$ and $BAF$ are congruent, hence the area of quadrilateral $JKEB$ and the area of square $BCGF$ are equal, hence $AB^2 = AC^2 + BC^2$ (the Pythagoras Theorem).

Accepted Answer

$\text{(i)}\ \triangle DAC\cong\triangle BAI\text{ (SAS)}$ $\text{(ii)}\ \operatorname{Area}(ADKJ)=\operatorname{Area}(ACHI)$ $\text{(iii)}\ \triangle BEC\cong\triangle BAF\text{ (SAS)}$ $\text{(iv)}\ \operatorname{Area}(JKEB)=\operatorname{Area}(BCGF)$ $\text{(v)}\ AB^2=AC^2+BC^2$

IP2U8 HOT Q4 (Euclid's Proof of the Pythagoras' Theorem)

IP2U8 HOT Q4 (Euclid's Proof of the Pythagoras' Theorem)

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