Question

the perpendicular bisector of AB is m and the perpendicular bisector of BC in n. Lines m and n intersect at T. idv TA=8.2, whats is TC?

Answer 1

Since lines m and n are perpendicular bisectors of AB and BC, and they intersect at T, triangles ATB and BTC are congruent. Thus, TA equals TC, so TC is also 8.2 units long.

Step-by-step explanation:

Since lines m and n are the perpendicular bisectors of AB and BC respectively, and they intersect at point T, triangle ATB and triangle BTC are congruent by the Side-Side-Side (SSS) Congruence Theorem. This is because AB equals BC (as given), TB is common in both triangles, and AT and TC are the halves of the respective bisected lines, which means they are also equal.Given TA = 8.2, and because triangle ATB is congruent to triangle BTC, TC must also be equal to TA. Therefore, TC is also 8.2 units long.