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Proving Triangles are Congruent SSS and SAS

Similar Triangles:

When two triangles have the same shape but different sizes they are referred to as similar triangles. Symbolically, it can be written as, "~".

Congruent Triangles:

When two triangles have the same shape and same size they are referred to as congruent triangles. They are also referred to as the special type of similar triangles.

Two triangles are said to congruent if,

• All 6 pairs of corresponding angles and sides are congruent.
• All 3 pairs of corresponding sides are the same.

Side Angle Side Congruence Postulate:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are said to be congruent.

What is an included angle?

An included side means the side included between the angles.

Consider the following example:

Prove, ΔDEF is congruent ΔGHI, that is, ΔDEF = ΔGHI. Proof:

• Two sides and the included angle are congruent.
• DE = GH (side)
• DEF = GHI (angle)
• EF = HI (side)
• Hence by the side angle side postulate (SAS), the two triangles are congruent.

Side Side Side Postulate: If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent. Consider the following example: Prove that ΔDEF is congruent toΔGHI, that is, ΔDEF = ΔGHI

Proof: To prove:ΔDEF = ΔGHI

• All the 3 sides are congruent i.e.,
•  IG = FD (side)
• GH = DE (side)
• HI  = EF (side)
• Hence, by the Side Side Side postulate, the triangles are said to be congruent.
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