Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.

A line has points A, C, B.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the
congruence
property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.

Question

13-06-2022
Mathematics

contestada

Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.

A line has points A, C, B.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the
congruence
property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.

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Martebi Martebi · Answer 1 · 2022-06-24T20:18:51+02:00

In proving that C is the midpoint of AB, we see truly that C has Symmetric property.

What is the proof about?

Note that:

AB = 12

AC = 6.

BC = AB - AC

= 12 - 6

=6

So, AC, BC= 6

Since C is in the middle, one can say that C is the midpoint of AB.

Note that the use of segment addition property shows: AC + CB = AB = 12

Since it has Symmetric property, AC = 6 and Subtraction property shows that CB = 6

Therefore, AC = CB and thus In proving that C is the midpoint of AB, we see truly that C has Symmetric property.

See full question below

Given: AB = 12 AC = 6 Prove: C is the midpoint of AB. A line has points A, C, B. Proof: We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments. Answer choices: Congruence Symmetric Reflexive Transitive

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