Geometry 5-4 Complete Lesson: Medians and Altitudes

By Matthew Richardson

Last updated over 3 years ago

24 questions

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! Draw a large acute scalene △ABC. On each side, mark the point that is ⅕ of the distance from one of the side's endpoints, as shown in the diagram. Connect each fo these points to the opposite vertex. Repeat this process for ¼ and ⅓. What do you think think the results will be for ½? Explain.

Solve It! Check your answer. Were you correct?

Problem 1 Got It? In the diagram for Problem 1, ZA = 9. What is the length of segment ZC? Enter only a number. Use decimal form, if necessary.

Problem 1 Got It? Reasoning: What is the ratio of ZA to AC? Explain.

Problem 2 Got It?

Problem 3 Got It?

Reasoning: Does it matter which two altitudes you use to locate the orthocenter of a triangle? Explain.

Reasoning: The orthocenter of △ABC lies at vertex A. What can you conclude about segment BA and segment AC? Explain.

Review Lesson 5-3: Is segment XY a perpendicular bisector, an angle bisector, or neither?

Review Lesson 2-2: Match the statemens on the left with their negations on the right. Each statement should only be used once.

Two angles are congruent.
You are not 16 years old.
m∠A < 90

m∠A > 90
Two angles are not congruent.
You are 16 years old.
m∠A ≥ 90
You are 17 years old.

Vocabulary Review: Use Yes and No to respond to each question.

Are three diameters of a circle concurrent?
Are two diagonals of a rectangle concurrent?
Is the intersection of three streets a point of concurrency?

Use Your Vocabulary: Label each statement as True or False.

True
False

The median of a triangle is a segment that connects the midpoint of one side to the midpoint of an adjacent side.
The point of concurrency of the medians of a triangle is where they intersect.
A triangle has only one median.

Geometry 5-4 Complete Lesson: Medians and Altitudes

Solve It! Check your answer. Were you correct?

Problem 1 Got It? In the diagram for Problem 1, ZA = 9. What is the length of segment ZC? Enter only a number. Use decimal form, if necessary.

Problem 1 Got It? Reasoning: What is the ratio of ZA to AC? Explain.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It?

Reasoning: Does it matter which two altitudes you use to locate the orthocenter of a triangle? Explain.

Reasoning: The orthocenter of △ABC lies at vertex A. What can you conclude about segment BA and segment AC? Explain.

Review Lesson 5-3: Is segment XY a perpendicular bisector, an angle bisector, or neither?

Review Lesson 5-3: Is segment XY a perpendicular bisector, an angle bisector, or neither?

Review Lesson 2-2: Match the statemens on the left with their negations on the right. Each statement should only be used once.

Vocabulary Review: Use Yes and No to respond to each question.

Use Your Vocabulary: Label each statement as True or False.

Your response should be in the form of two adjacent letters and not contain spaces.

Reflection: Math Success