# Construction Techniques 5: Squares

# Construction Techniques 5: Squares

##### Problem 1

1) Which of these statements is true?

##### Problem 2

2) This diagram is a straightedge and compass construction of a square $BACD$ (not all markings are shown). The construction followed these steps:

1. Start with two marked points $A$ and $B$

2. Use a straightedge to construct line $AB$

3. Use a previous construction to construct a line perpendicular to $AB$ passing through $A$

4. Use a previous construction to construct a line perpendicular to $AB$ passing through $B$

5. Use a compass to construct a circle centered at $A$ passing through $B$

6. Label an intersection point of that circle and the line from step 3 as $C$

7. Use a previous construction to construct a line parallel to $AB$ passing through $C$

8. Label the intersection of that line and the line from step 4 as $D$

9. Use a straightedge to construct the segments $AC$, $CD$, and $DB$

Explain why you need to construct a circle in step 5.

##### Problem 3

3) To construct a line passing through the point $C$ that is parallel to the line $AB$, the first step is to create a line through $C$ perpendicular to $AB$. What is the next step?

##### Problem 4

4) Jada wanted to construct a line perpendicular to line $l$ through point $C$. The diagram shows her construction. What was her mistake?

##### Problem 5

5) Noah is trying to bisect angle $BAC$. He draws circles of the same radius with centers $B$ and $C$ and then uses one of the points of intersection for his ray. What mistake has Noah made in his construction?

##### Problem 6

6) Here is a straightedge and compass construction. Use a straightedge to draw an equilateral triangle on the figure.

7) Explain how you know the triangle is equilateral.

##### Problem 7

8) Here are 2 points in the plane. Explain how to construct a line segment that is half the length of segment $AB$.