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Congruency & Similarity
O-Level E Math
Proof of Congruent Triangles
Valid methods:
SSS, SAS, ASA, AAS, RHS
✗ ASS is not valid
Proof of Similar Triangles
All ratios of corresponding sides are equal.
Two ratios of sides + included angle are equal.
Two angles are equal (AA).
Similar Figures & Solids
$$\dfrac{A_1}{A_2} = \left(\dfrac{l_1}{l_2}\right)^2$$
Similar figures — area ratio
$$\dfrac{V_1}{V_2} = \left(\dfrac{l_1}{l_2}\right)^3$$
Similar solids — volume ratio
Similar Triangles
$$\text{Ratio of area} = \left(\text{Ratio of length}\right)^2$$
A
B
a
b
$\dfrac{\text{Area }A}{\text{Area }B} = \left(\dfrac{a}{b}\right)^2$
Triangles with the Same ⊥ Height
$$\text{Ratio of area} = \text{Ratio of bases}$$
A
B
a
b
$\dfrac{\text{Area }A}{\text{Area }B} = \dfrac{a}{b}$
Formulas for the Singapore O-Level Elementary Mathematics syllabus