Congruent shapes are those which have the same shape and size. These shapes can be rotated to look different but remain congruent.
The Congruent shapes if are reflections (mirror image) of each other they might look very different.
Watch: Congruent Triangles
Congruent Triangles
Congruent Triangles are those which are same in size and shape but their orientation maybe different.
Examples:
Congruent Triangle Rules
We cannot always tell by just seeing the Triangles that they are congruent or not. Thus we have following Rules and by learning them we can easily detect the Congruent Triangles.
S – Side
A – Angle
R – Right Angle
H – Hypotenuse
1. SSS
All sides are equal in length.
2. SAS
When two sides and the angle between them is same in both the triangles.
3. AAS
Two Angles are same and one side is equal in both triangles at the same place with respect to these two equal angles.
4. RHS
When one of the angles is Right angle and Hypotenuse lengths are same along with one equal side.
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Detect the congruent triangles among the following triangles? (Part a)
SOLUTION
Final Answer: 2nd and 4th Triangles are Congruent (by SSS).
Solved Example
Detect the congruent triangles among the following triangles? (Part b)
SOLUTION
Final Answer: 1st and 3rd Triangles are Congruent (by SAS).
Solved Example
Detect the congruent triangles among the following triangles? (Part c)
SOLUTION
Final Answer: 1st and 3rd Triangles are Congruent (by RHS) their orientation is different but still size and shape is same.
Solved Example
Detect the congruent triangles among the following triangles? (Part d)
SOLUTION
Final Answer: 1st and 4th Triangles are Congruent (by AAS) their orientation is different but still size and shape is same.
Solved Example
Given that the following Triangles are congruent, then find out the missing side in the triangle B?
SOLUTION
The above triangles are congruent by the rule RHS as both the triangles are right angle triangles and two sides are equal one of them being hypotenuse. The second triangle’s hypotenuse is equal to the hypotenuse of the first triangle.
Thus, $x = 7$ cm
Final Answer: $x = 7$ cm
Solved Example
Given that the following Triangles are congruent, then find out the missing side in the triangle A?
SOLUTION
The triangles are congruent by the rule SSS means the sides are equal.
Thus, $x = 3$ cm.
Final Answer: $x = 3$ cm
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