Congruence Test – O Level Exam Preparation Guide
In this Congruence Test revision note, you will learn the steps for different congruence tests and the properties of Congruent triangles.
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Congruent Figures
- Two geometric figures are congruent if they are of the same shape and size.
- When two figures undergoes a rotation, reflection, or translation, the shape and size remains the same. Hence, they are congruent to each other.
Congruent triangles properties
ΔABC ≡ ΔDEF (Note that the order matters)
if and only if…
corresponding sides are equal,
AB = DE , AC = DF and BC = EF
and corresponding angles are equal.
∠A = ∠D , ∠B = ∠E and ∠C = ∠F
Congruence Test
Here are 4 important congruence tests.
1. Side ‒ Side ‒ Side
∠A = ∠D AB = DE
∠B = ∠E BC = EF
∠C = ∠F AC = DF
∆ABC coincide with ∆DEF
So ∆ABC ≅ ∆DEF (SSS Rule)
2. Angle ‒ Side ‒ Angle
Let BC = EF, ∠B = ∠E, AB = DE, ∠C = ∠F
So ∆ABC ≅ ∆DEF (ASA Rule)
3. Side ‒ Angle ‒ Side
AB = EF
∠ABC = ∠EFG
BC = FG
So ∆ABC ≅ ∆EFG (SAS Rule)
Note: The angle must be in between the 2 sides.
4. Right angled ‒ Hypotenuse ‒ Side
∠B = ∠Y = 90°
AB = XY
AC = XZ
So ∆ABC ≅ ∆XYZ (SAS Rule)
Congruent Triangles Examples
In ∆ABC and ∆ABD,
BC = AD
AC = BD
AB is common
∴ ∆ABC ≡ ∆ABD (SSS)
In ∆ABE and ∆FCE,
AB = FC
∠BAE = ∠CFE
∠AEB = ∠FEC (vertically opposite angles)
∴ ∆ABE ≡ ∆FCE (AAS)
In ∆ABC and ∆DEF,
AB = DE
BC = EF
∠ABC = ∠DEF
∴ ∆ABC ≡ ∆DEF (SAS)
In ∆ABC and ∆DCE,
∠ACB = ∠ DCE = 90°
AB = DE (Hypotenuse)
AC = DC
∴ ∆ABC ≡ ∆DCE (RHS)
Last Minute Revision for O Level Math?
Check out our exam guide on other topics here!
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