Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ABC= XYZ

 A) SAS  and   B) ASA  and   (D) LA

Step-by-step explanation:

A) AC = XZ  Sides are congruent

   ∠C = ∠Z   Angles are congruent

   BC = YZ   Sides are congruent  

                  Side-Angle-Side

B) ∠A = ∠X   Angles are congruent

    AC = XZ   Sides are congruent

   ∠C = ∠Z   Angles are congruent  

                  Angle-Side-Angle

C) AB = XY is not given. We can use Pythagorean Theorem to discover that they are the same but since it is not given we cannot use Side-Side-Side.

D) AC = XZ   Legs are congruent

    ∠A = ∠X   acute Angles are congruent  

                     Leg-Angle

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for