Honors Geometry Unit 4 Project 1 - Part 5

Part 5A•On a sheet of paper, construct a scalene

triangle of sides 14cm, 12cm and 10cm.

•Label the vertices A, B, and C.

•Find the midpoint of AC, BC and AB.

•Label these midpoints P, Q and R, respectively.

•Draw perpendicular lines through P, Q and R.

•These lines will not necessarily pass through any of the vertices of the triangle

Part 5A Analysis

•Answer the question on the answer sheet.

Part 5B

•Label the Point of Concurrency S

•Draw segments AS, BS and CS

•Measure AS, BS and CS and record

Part 5C

•Using your compass, draw a circle with a center at S that contains points A, B and C

•Record your observations

Part 5D•Repeat Parts 5A, 5B and 5C for:

•An obtuse scalene triangle

•A right scalene triangle

•An isosceles triangle

•An equilateral triangle

•Record your observations on the answer sheet.

Part 5E•Each member of the group is to draw 3 segments

such that all nine are different lengths, label them each AB.

•Find the midpoints of each segment and label teach of them M.

•Then draw a perpendicular line through each of the midpoints

•Pick a points on each perpendicular line and label it C

•draw segments AC and BC

•Measure AC and BC and record on the answer sheet

Part 5E (cont.)

•Pick another point on the perpendicular line and label it D

•draw segments AD and BD

•Measure AD and BD and record on the answer sheet

•Answer the follow up question on the answer sheet

Perpendicular Bisector

(of a segment!)

•A line, ray or segment that is perpendicular to and bisects a segment is a perpendicular bisector of the segment.

The Perpendicular Bisector Theorem

•Any point on the perpendicular bisector of a segment is equidistant form the end points of the segment.

The Perpendicular Bisectors and a

triangle•The point of concurrency of the of

the perpendicular bisectors is called the circumcenter

•The circumcenter is the center of the circumscribed circle aka the circumcircle. (circumscribed - to be drawn around)

Part 6A•Looking through all of the triangles

you have produced so far, choose the type whose points of concurrency are:

•separate points

•all on the interior of the triangle

•Check with the instructor before continuing on to the nect step

Step 6B• Each student is to do the following!

• On each of 4 notecards (one triangle per card), draw congruent triangles of the type chosen on the previous page (draw them reasonably large - try to fill most of the card)

• one the first card, draw the 3 medians

• one the second card, draw the 3 altitudes

• one the third card, draw the 3 angle bisectors

• one the fourth card, draw the 3 perp. bisectors

Part 6B (cont.)•Cut out each of the triangles drawn on your

cards

•poke a pin hole through the point of concurrency in each triangle

•cut 4 lengths of orange string about 4-6in. long

•thread the string through the hole and tie a knot

Part 6B (cont.)

•Hang each triangle by its string and observe what happens

•Record your observations on the answer sheet

Part 6B Analysis

•Answer the questions on the answer sheet

Project Analysis

•Type up the following:

•What did you learn from this project?

•(separate paragraph per team member!)

To turn-in

•Due Tuesday, January 11, 2011

•All answer sheets

•All triangles produced including the Cut-out triangles

•Personal Reflections