Write 4–6 sentences explaining why it is important to have precise definitions in mathematics. Choose five terms, some from geometry and some from other areas of mathematics, and give a precise definition of each. Then change each of those definitions so that it still describes the term but not precisely enough to avoid ambiguity. Formulate counterexamples, with sketches when feasible, that show how things could satisfy the less precise definitions but not match the intended terms.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

the scale is 1/9 my friend can't simplify 1 anymore so it will be (for every 1 there's 9)

it changed by a factor of 2.

the measure of the unknown angle is 7.5