Geometry 5-4 Medians and Altitudes

by Matthew Richardson

| 24 QuestionsNote 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.

1

2

1

10 pts

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.

2

5 pts

Solve It! Check your answer. Were you correct?

3

4

3

10 pts

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.

4

10 pts

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

5

5

10 pts

Problem 2 Got It?

A

B

C

D

6

6

10 pts

Problem 2 Got It?

A

B

C

D

7

7

10 pts

Problem 2 Got It?

A

B

C

D

8

8

10 pts

Problem 3 Got It?

A

B

C

D

9

9

10 pts

A

B

10

10

10 pts

A

B

C

D

11

11

10 pts

A

B

C

D

12

12

10 pts

A

B

C

D

13

14

10 pts

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

15

10 pts

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

16

16

10 pts

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

perpendicular bisector

angle bisector

neither

17

17

10 pts

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

perpendicular bisector

angle bisector

neither

18

10 pts

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.

19

10 pts

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

- Yes
- No

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

20

10 pts

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.

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23

21

5 pts

GE

HC

EF

DJ

22

5 pts

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

23

5 pts

⅔(CH)

⅔(FH)

CH

⅔(EG)

24

10 pts

Reflection: Math Success

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