Question

Given AB congruent to CD. State wheather AC congruent to BD and why.​

Answer 1

Solution:-

We know that if two lines congruent ( AB ≅ CD ) It means they are equal in measure that is,

AB = CD     ------- (i)

Now, From equation (i) we get,

AB + BC = CD + BC             [ If equals are added to the equals then the wholes are equal ( Euclid's second axiom ) ]

∴ AC = BD        [ AB + BC = AC       and      CD + BC = BD ]

Hence, We know if two lines are equal in measure ( AC = BD ) It means they congruent that is,

AC ≅ BD

   ------     Proved

Some important terms:-

• Euclid's given Seven Axioms that are:-

1. Things which are equal to the same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.
6. Things which are double of the same things are equal to one another.
7. Things which are halves of the same things are equal to one another.

Answer 2

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