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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Why SAS congr...

Question

Why SAS congruence rule is stated as an Axiom and other rules are stated as Theorems?

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Solution

We call SAS congruence rule an axiom as we see that it is universally true and we do not prove this. We learn when we can say that any two given triangles ABC and PQR are congruent as per SAS congruence rule. We also see that if two triangles are congruent, then their corresponding sides and angles are also equal.

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In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

If two right-angled triangles have their hypotenuses and one side equal,
then the two triangles are congruent by SAS congruence rule.

In the given figure, which congruence rule can be used to prove that $△$ ABC $≅$ $△$ CDA?

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