# AHSA Geometry Questions; triangles and centers

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### Question Description

I have included the rubric for these questions, so please follow the guidelines. I need clear and detailed work. I have included the page that these questions I mentioned are on, with the corresponding images that go with these tasks that are part of the question. Please make sure again, detailed work, and create images, graphs etc if applicable per question. Thank you very much!

Task 1 - Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. Th e campsites have the following coordinates: Brighton Bluff at B(2, 2), Ponaganset Peak at P(4, 10), and Harmony Hill at H(12, 2). He wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the showers should be placed

You can use proven theorems to explore relationships among sides, angles, and special lines and segments in triangles.

a. Draw nABC with obtuse /C and construct its orthocenter O. Then find the orthocenters of nABO, nACO, and nBCO. What did you discover? Explain why you get this result.

b. Will your conjecture be true for any acute or right nABC? Explain your reasoning

You can use indirect reasoning to prove relationships within triangles.

Task 3 - In nABC, AB 2 BC. Show that there does not exist a point P on altitude BD that is equidistant from A and C.

5 To solve these problems you will pull together many concepts and skills that you have studied about relationships within triangles. Pull It All Together Coordinate Geometry You can use the Midpoint Formula, the slope formula, and the relationship between perpendicular lines to find points of concurrency. Task 1 Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. The campsites have the following coordinates: Brighton Bluff at B(2, 2), Ponaganset Peak at P(4, 10), and Harmony Hill at H(12, 2). He wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the showers should be placed. Reasoning and Proof You can use proven theorems to explore relationships among sides, angles, and special lines and segments in triangles. Task 2 a. Draw nABC with obtuse /C and construct its orthocenter O. Then find the orthocenters of nABO, nACO, and nBCO. What did you discover? Explain why you get this result. b. Will your conjecture be true for any acute or right nABC? Explain your reasoning. Reasoning and Proof You can use indirect reasoning to prove relationships within triangles. Task 3 In nABC, AB 2 BC. Show that there does not exist a point P on altitude BD that is equidistant from A and C. B A 340 Chapter 5 Pull It All Together Copyright © 2011 Pearson Education, Inc. D C
Unit 5 Project Rubric Task 1 Determines type of triangle center that is point equidistant from all three points. 1 point Finds correct coordinates of point equidistant from all three points. 1 point Uses diagram and/or shows algebra to find point. 3 points Total 5 points Task 2 Constructs diagram using straightedge and compass and finds the orthocenter O. 2 points Determines the relationships between the orthocenters of the 3 new triangles correctly. 3 points Answers part b correctly and gives a valid and clear justification. 3 points Total 8 points Task 3 Writes an indirect proof 2 points Uses theorems learned in unit to justify statements in the proof. 2 point Proof is complete and valid 2 points Total 6 points

proggerardo
School: Boston College

Attached you will find the outline and answers of your assignment. Please let me know if you need modifications or clarification.

5
To solve these
problems you
will pull together
many concepts
and skills
that you have
relationships
within triangles.

Pull It All Together
Coordinate Geometry
You can use the Midpoint Formula, the slope formula, and the relationship between
perpendicular lines to find points of concurrency.

Your math teacher manages a campground during summer vacation. He loves math so
much that he has mapped the campground on a coordinate grid. The campsites have
the following coordinates: Brighton Bluff at B(2, 2), Ponaganset Peak at P(4, 10), and
Harmony Hill at H(12, 2). He wants to build showers that are equidistant from all three
campsites. Find the coordinates of the point where the showers should be placed.

Reasoning and Proof
You can use proven theorems to explore relationships among sides, angles, and special
lines and segments in triangles.

a. Draw nABC with obtuse /C and construct its orthocenter O. Then find the
orthocenters of nABO, nACO, and nBCO. What did you discover? Explain why
y...

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Anonymous
awesome work thanks

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