Concept Byte: Exploring Constructions

Use With Lesson 1-6

TECHNOLOGY

You can use Draw tools or Construct tools in geometry software to make points, lines, and planes. A figure made by Draw has no constraints. When you manipulate, or try to change, a figure made by Draw, it moves or changes size freely. A figure made by Construct is related to an existing object. When you manipulate the existing object, the constructed object moves or resizes accordingly.

In this Activity, you will explore the difference between Draw and Construct.

Activity

Draw A B ¯ eh b bar  and Construct the perpendicular bisector D C ↔ . modified d c with left right arrow above , .  Then Draw E F ¯ e f bar  and Construct G, any point on E F ¯ . e f bar , .  Draw H G ↔ . modified h g with left right arrow above , .

1. Find EG, GF, and m ∠ HGF . m angle  Try to drag G so that E G = G F . e g equals g f .  Try to drag H so that m ∠ HGF = 90 . m angle  Were you able to draw the perpendicular bisector of E F ¯ ? e f bar , question mark  Explain.
2. Drag A and B. Observe AC, CB, and m ∠ DCB . m angle  Is D C ↔ modified d c with left right arrow above  always the perpendicular bisector of A B ¯ eh b bar  no matter how you manipulate the figure?
3. Drag E and F. Observe EG, GF, and m ∠ HGF . m angle  How is the relationship between E F ¯ e f bar  and H G ↔ modified h g with left right arrow above  different from the relationship between A B ¯ eh b bar  and D C ↔ ? modified d c with left right arrow above , question mark
4. Write a description of the general difference between Draw and Construct. Then use your description to explain why the relationship between E F ¯ e f bar  and H G ↔ modified h g with left right arrow above  differs from the relationship between A B ¯ eh b bar  and D C ↔ . modified d c with left right arrow above , .

Exercises

5. 1. Draw ∠ NOP . angle  Draw O Q → o q vector  in the interior of ∠ NOP . angle  Drag Q until m ∠ NOQ = m ∠ QOP . m angle
   2. Manipulate the figure and observe the different angle measures. Is O Q → o q vector  always the angle bisector of ∠ NOP ? angle
6. 1. Draw ∠ JKL . angle
   2. Construct its angle bisector, K M → . k m vector , .
   3. Manipulate the figure and observe the different angle measures. Is K M → k m vector  always the angle bisector of ∠ JKL ? angle
   4. How can you manipulate the figure on the screen so that it shows a right angle? Justify your answer.

   

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