2.5.3 Journal: Proofs of Congruence The Engineers' Conjectures: The engineers are designing a bridge truss, and they need to prove that two triangles inside the truss are congruent. 1. Complete the table to summarize what you know about each engineer's conjecture: (2 points: 1 point for each row of the chart) Engineer Conjecture Natalie Emma 2. Analyze the conjectures. Who do you think is correct, and why? (1 point) Analyzing the Data 3. Here is a picture of the bridge truss, and the given information: Fill out the two-column proof to prove that BED BEF. You may not need to use all the rows. (5 points) Statement Reason 4. State how you know that BDF is an isosceles triangle. (2 points) 5. Using the previous problem, fill out the two-column proof that ABD CBF. You may not need to use all t

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Jessica is asked to write a quadratic equation to represent a function that goes through the point (8, –11) and has a vertex at (6, –3). Her work is shown below. –11 = a(8 – 6)2 – 3 –11 = a(2)2 – 3 –11 = 4a – 3 –8 = 4a a = –2 After Jessica gets stuck, she asks Sally to help her finish the problem. Sally states that Jessica needs to write the quadratic equation using the value she found for a, –2, and the point (8, –11). Evaluate Jessica’s work and Sally’s review to determine which statement is true. 1. Jessica did not solve for the correct value of a, but Sally’s review is correct. 2. Jessica did not solve for the correct value of a, and Sally’s review is incorrect. 3. Jessica solved for the correct value of a, but Sally’s review was incorrect. 4. Both Jessica’s work and Sally’s review are correct. The equation is f(x) = –2(x – 8)2 – 11.

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Which ordered pair is a solution to this equation?2x + 3y = 16A. (5, 2)B. (3, 2)C. (11, 1)D. (7, 2)The equation of a line is −2x+5y=−20.What is the x-intercept of the line?Enter your answer in the box._________What is the slope of the line passing through the points (2, −5) and (4, 1)?A. 3B. ​−45 ​C. 54 ​ D. 2Select all statements that are true about the linear equation.y = 4x − 3______ The graph of the equation is the set of all points that are solutions to the equation._______ The point (0, −3) is on the graph of the equation.________The point (1, 1) is on the graph of the equation._______ The graph of the equation is a single point representing one solution to the equation.

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