Warm UpUsing a compass, create one of each of the following:

Duplicate an angle:

Construct a perpendicular bisector:

Construct a perpendicular to a line from a point:

Student of the dayBlock 4

Student of the dayBlock 5

Student of the dayBlock 6

Review Homework pg 155 #1-5; pg 218 and 219 #1-10

H.W. Answers continued..

3.4 Constructing an Angle Bisector

Method 1: FoldingStep 1: Using the patty paper, create your own

angle using a straightedge.Step 2: Fold the patty paper so that the two legs lie

on top of one another.Step 3: Draw a line down the crease

This is our angle bisector.

3.4 Constructing an Angle Bisector

Method 2: Using a compassStep 1: Put the point of the compass on the vertex

of the angle given and create two intersection points with the legs of the angle.

Step 2: With these two intersections do the same steps as you would for perpendicular bisector

Step 3: What observations can you make from this?

Conjecture C-7: Shortest Distance ConjectureThe shortest distance from a point to a line is

measured along the ______________ from the point to the line.

Conjecture C-8: Angle Bisector ConjectureIf a point is on the bisector of an angle, then it is

_____________ from the sides of the angle.

4.4 Congruence Shortcuts

How many parts do we need congruent for both triangles to be congruent?

6 parts?5 parts? 4 parts?3 parts?2 parts?1 parts?0 parts?

Combinations of three

(SSS) Side – Side – Side(SAS) Side – Angle – Side(ASA) Angle – Side – Angle (SAA) Side – Angle – Angle (SSA) Side – Side – Angle (AAA) Angle – Angle – Angle

SSS InvestigationThe length of each leg will be 2 inches, 3 inches and 4 inches

Instructions:1. Pick a length and use a straightedge to create this length near the

bottom of the paper. (to make sure we have enough room for the triangle)

2. Pick another length and measure the compass to this length.3. Put the point of the compass on an endpoint of your original line

and create a very large arc.4. Pick the last length and measure the compass to this length.5. Put the point of the compass on the other endpoint of your original

line and create a very large arc.6. The intersection of the two arcs will be the third point of your

triangle.7. Draw your triangle.8. Check to make sure the three legs of the triangle are actually 2,3,

and 4 inches.9. Cut out the triangle.

Conjecture C-23: SSS Congruence ConjectureIf the three sides of one triangle are congruent

to the three sides of another triangle, then ____________.

Conjecture C-24

Conjecture C-24: SAS Congruence ConjectureIf two sides and the included angle of one

triangle are congruent to two sides and the included angle of another triangle, then ______________.

SAS Investigation

The length of the two legs will be 2 and 4 inches, the angle will be 40 degrees

Instructions:1. Create your angle of 40 degrees using your protractor2. From the vertex measure a length of 2 or 4 inches along one of the

legs.3. From the vertex measure the other length along the other leg

We now have a 40 degree angle with legs of 2 and 4 inches.5. Using a straightedge and the endpoints of the legs create the third side

of the triangle.5. Cut out the triangle.6. Compare with three other triangles.

Quiz Directions1) Complete both sides.2) Show your arcs on the construction side for credit3) When you finished turn your quiz in at the front of the

classroom.FORM A1st picture is for #15, 2nd picture is for #16Use this for #17.

Start the h.w. pg 160 #1- 5 and #10 pg 224 #4-9, #12 – 17