how do you write out proofs?

To be more specific with my question, how do you find the alternate exterior angles theorem?

Be sure the result is not a postulate. If it is then there's nothing to prove, it's given. If it is a theorem -a provable statement- then review the avialable definitions, postulates and theorems to find a proof strategy. Generally, proving theorems is a trial and error process and you should improve in your ability to write them with practice.

ok so there is an isosceles triangle with altitude 'cd' and the left angle is 'a' and the right is 'b'. ok so if 'ad' is 4m and if 'db' is 9m then wat is 'cd' and how do u get it?

To find the length of the altitude 'cd' in the isosceles triangle, we can use the Pythagorean Theorem.

First, let's draw the triangle and label the given lengths:

C
/ \
/ \
a / \ b
/_______\
D

Given:
ad = 4m
db = 9m

In an isosceles triangle, the altitude from the vertex to the base (cd in this case) is also the perpendicular bisector of the base (ab in this case). So, cd bisects ab at point D.

Since cd bisects ab, we can divide the base into two congruent segments, making ad and db each half of the base. Therefore, ad = db = (4m + 9m) / 2 = 13m / 2 = 6.5m.

Now, let's use the Pythagorean Theorem to find the length of the altitude 'cd'. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In triangle CDB, cd is the hypotenuse, ad is one side, and db is the other side. So, we have:

cd^2 = ad^2 + db^2

Plugging in the values:

cd^2 = (6.5m)^2 + (9m)^2

Simplifying:

cd^2 = 42.25m^2 + 81m^2

cd^2 = 123.25m^2

Taking the square root of both sides to find 'cd':

cd = √(123.25m^2)

cd ≈ 11.10m

Therefore, the length of the altitude 'cd' is approximately 11.10m.