The provided diagram of triangle abc will you to prove that the base angles of an isosceles triangle are congruent. the first step is to draw auxiliary line ao. what must be true about in order to complete the proof using the asa (angle side angle) triangle congruency theorem? classify each statement as needed or not needed to complete the proof. ao bisects bac ao is perpendicular to bc point o is the midpoint of bc ao is an altitude. answer choices are: needed not needed

I did this:

1. Needed

2. Needed

3. Not Needed

4. Needed

Step-by-step explanation:

AO bisects BAC - Needed

AO is perpendicular to BC  - Needed

Point O is the midpoint of BC  - Not needed

AO is an altitude - Not needed

Step-by-step explanation:

In ΔAOB,

In ΔAOC,

In ΔAOB and ΔAOC,

So, we can conclude ΔAOB ≅ ΔAOC (ASA property) and hence the base angles <ABO and < ACO of the isosceles triangle ABC are also congruent.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.