1. ©G Dear2010 – Not to be sold/Free to use
Congruence
Triangles
Properties
Stage 4 - Year 9
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©G Dear2010 – Not to be sold/Free to use

2. Two triangles are congruent if they are the same size and shape.
Congruent Triangles
Two triangles are congruent if they are the same size and shape.
There are four Rules
Side, Side, Side.
Side, Angle, Side.
Angle, Angle, Side.
Right Angle, Hypotenuse, Side.
End of
Slide

3. Prove that the base angles of an isosceles triangle are equal.
Isosceles Triangles
Prove that the base angles of an isosceles triangle are equal. A B C
Add a perpendicular. D
ADB = ADC
Right Angle
AB = AC
Hypotenuse
AD = AD
Common Side
ADB  ADC
RHS ● ●
B = C
Congruent s
End of
Slide

4. Equilateral Triangles
Prove that the sides of an equilateral triangle are equal.
Add a bisector. A B C
60o
B = C
Given Angle D
ADB = ADC
Right Angle
AD = AD
Common Side ● ●
ADB  ADC
AAS
AB = AC
Congruent s
Repeat for each side.
End of
Show
 AB = BC = AC