How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof?

• Triangle Sum Theorem
• Triangle Inequality Theorem
• Isosceles Triangle Theorem
• Converse of the Isosceles Triangle Theorem
• Midsegment of a Triangle Theorem
• Concurrency of Medians Theorem

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.

Apolygon is shown on the graph: a polygon is shown on the coordinate plane. vertices are located at 3 comma 5, 1 comma 3, 1 comma 1, 2 comma 0, 4 comma 0, 5 comma 1, and 5 comma 3. what effect will a translation 3 units down and 2 units left have on the polygon? be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image. xd i need

Use pascal's triangle to find the missing values. x4 - 4xb + 6x2 - ax + 1