Geometry 5-3 Complete Lesson: Bisectors in Triangles

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Construct a circle and label its center C. Choose any three points on the circle and connect them to form a triangle. Draw three lines from C such that each line is perpendicular to one side of the triangle. What conjecture can you make about the two segements into which each side of the triangle is divided? Justify your reasoning.

Problem 2 Got It? In Problem 2, the town planner wants to place a bench equidistant from the three trees in the park. Where should he place the bench?

Problem 3 Got It? QN = 5x + 36 and QM = 2x + 51. What is QO? Enter only a number.

Problem 3 Got It? Reasoning: Is it possible for QP to equal 50? Explain.

Vocabulary: A triangle's circumcenter is outside the triangle. What type of triangle is it?

Reasoning: You want to find the circumcenter of a triangle. Why do you only need to find the intersection of two of the triangle's perpendicular bisectors, instead of all three?

Error Analysis: Your friend sees the diagram and concludes that CT = CP. What is the error in your friend's reasoning?

Compare and Contrast: How are the circumcenter and incenter of a triangle alike? How are they different?

Review Lesson 5-2: Find the value of x. Enter only a number.

Review Lesson 5-2: Find AD. Enter only a number.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.
Enter your answer in this format, (3, 5.2), with the only space being immediately after the comma.

Use Your Vocabulary: Complete each statement with concurrency, concurrent, or concurrently.

concurrency
concurrent
concurrently

Two classes are __?__ when they meet at the same time.
The point of __?__ of three streets is the intersection of the streets.
A person may go to school and hold a job __?__.

Use Your Vocabulary: Categorize each diagram as concurrent or not concurrent.

concurrent
not concurrent

Problem 1 Got It?

Problem 2 Got It? In Problem 2, the town planner wants to place a bench equidistant from the three trees in the park. Where should he place the bench?

Problem 3 Got It? QN = 5x + 36 and QM = 2x + 51. What is QO? Enter only a number.

Problem 3 Got It? Reasoning: Is it possible for QP to equal 50? Explain.

Vocabulary: A triangle's circumcenter is outside the triangle. What type of triangle is it?

Reasoning: You want to find the circumcenter of a triangle. Why do you only need to find the intersection of two of the triangle's perpendicular bisectors, instead of all three?

Error Analysis: Your friend sees the diagram and concludes that CT = CP. What is the error in your friend's reasoning?

Compare and Contrast: How are the circumcenter and incenter of a triangle alike? How are they different?

Review Lesson 5-2: Find the value of x. Enter only a number.

Review Lesson 5-2: Find AD. Enter only a number.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.
Enter your answer in this format, (3, 5.2), with the only space being immediately after the comma.

Use Your Vocabulary: Complete each statement with concurrency, concurrent, or concurrently.

Use Your Vocabulary: Categorize each diagram as concurrent or not concurrent.

Reflection: Math Success

Geometry 5-3 Complete Lesson: Bisectors in Triangles

Problem 1 Got It?

Problem 2 Got It? In Problem 2, the town planner wants to place a bench equidistant from the three trees in the park. Where should he place the bench?

Problem 3 Got It? QN = 5x + 36 and QM = 2x + 51. What is QO? Enter only a number.

Problem 3 Got It? Reasoning: Is it possible for QP to equal 50? Explain.

Vocabulary: A triangle's circumcenter is outside the triangle. What type of triangle is it?

Reasoning: You want to find the circumcenter of a triangle. Why do you only need to find the intersection of two of the triangle's perpendicular bisectors, instead of all three?

Error Analysis: Your friend sees the diagram and concludes that CT = CP. What is the error in your friend's reasoning?

Compare and Contrast: How are the circumcenter and incenter of a triangle alike? How are they different?

Review Lesson 5-2: Find the value of x. Enter only a number.

Review Lesson 5-2: Find AD. Enter only a number.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.Enter your answer in this format, (3, 5.2), with the only space being immediately after the comma.

Use Your Vocabulary: Complete each statement with concurrency, concurrent, or concurrently.

Use Your Vocabulary: Categorize each diagram as concurrent or not concurrent.

Reflection: Math Success

Review Lesson 1-7: Find the coordinates of the midpoint of segment AB with the given endpoints.
Enter your answer in this format, (3, 5.2), with the only space being immediately after the comma.