Wednesday, November 28, 2018braunpaliszewski.weebly.com/.../2/4/4/8/24486951/03constrctionsda… ·...

Wednesday, November 28, 2018

• Warm-up• Name the following figures:

• More ConstructionsObjectives:Content: I will use basic constructions to better understand geometric properties.Social: I will work with others in my group, helping and listening for everyone to understand.Language: I will write steps clearly so that I can use them later.

Lesson 10: Construct a Parallel Line using a Perpendicular

Parallel lines never meet. Through the point P below, we can construct a lien that is parallel to the line l. We will use the theorem that two lines perpendicular to the same line are parallel.

Lesson 10: Construct a Parallel Line using a Perpendicular

1. Drop a perpendicular from P to line l. Label the new segment PC.(Follow the procedure from Lesson 8.) Extend this segment above P.

2. Erect a line through P perpendicular to PC. Label this new line PF. (Follow the procedure from Lesson 9.)

3. Lines l and PF are parallel, because they are both perpendicular to PC

Lesson 11: Construct a Square Given its Side

• A square is a special type of quadrilateral in which all four sides are the same length and two pairs of parallel sides. In Lesson 6, you constructed a square given its diagonal. Now, use what you know about constructing parallel and perpendicular lines to construct a square given its side. Build your square on side DC. Show all the constructions arcs you need - don’t erase them.

Lesson 11: Construct a Square Given its Side

Describe each step of your construction.

1. Erect a line through D perpendicular to CD. Label the line, m.

2.

3.

Brain Break

Lesson 12: Copying an Angle

To copy an angle means to construct an angle with the same measure but located somewhere else. You will copy angle A onto the line below.

Lesson 12: Copying an Angle

1. Set your compass to any convenient radius.

2. Draw an arc with center A that crosses both sides of angle A. Label the points where the arc crosses the side of the angle, B and C, with B above C.

3. Keeping the same radius, draw an arc with center X. Make the acr about the same length as the arc you drew in step 2. Label the point where the arc crosses the working line, Z.

4. Draw a short arc with center C passing through B, so that the radius of the compass is the length of BC.

5. Keeping the radius BC, draw an arc with center Z. Label the point where the two arcs cross, Y.

6. Draw XY.

Lesson 13: Construct a Parallel Line Using an Oblique Line

This construction shows that you don’t need perpendiculars to construct parallels. We will use an oblique line PB. (An oblique line is neither perpendicular nor parallel to a given line.)

To construct a parallel line through P, you will copy the angle with vertex B to a corresponding position with vertex P. Follow the steps below.

Lesson 13: Construct a Parallel Line Using an Oblique Line

1. Draw an arc with center B and passing through P. Label the point where the arc crosses the horizontal line, A.

2. Keeping the same radius, draw an arc with center P that crosses the oblique line above P and curves to the right. Label the point where the arc crosses the oblique line, Q.

3. Change the radius so you can draw an arc with center P that passes through A

4. Keeping the radius PA, draw an arc with center Q that crosses the other arc with center P. Label the point where the arcs cross, C.

5. Draw PC, which is parallel to the horizontal line. (Do you see that you have copied angle B?

Brain Break

Lesson 14: Challenge – Inscribing & Circumscribing Circles

• The point of concurrency of the three angle bisectors of any triangle is called the incenter. A circle centered at the incenter that touches all sides of this triangle is an inscribed circle. Using the triangle below, can you construct an inscribed circle?

Lesson 14: Challenge – Inscribing & Circumscribing Circles

• The point of concurrency of the three perpendicular bisectors of any triangle is the circumcenter. A circle centered at the circumcenter that touches all the vertices of this triangle is a circumscribed circle. Using the triangle below, can you construct an circumscribed circle?

Practice

Exit Slip