Warm Up Using 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 day Block 4

Student of the day Block 5

Student of the day Block 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: Folding Step 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 compass Step 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 Conjecture The shortest distance from a point to a line is measured along the ______________ from the point to the line. Conjecture C-8: Angle Bisector Conjecture If a point is on the bisector of an angle, then it is _____________ from the sides of the angle.

4.4 Congruence Shortcuts 6 parts? 5 parts? 4 parts? 3 parts? 2 parts? 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 Investigation The 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 Conjecture If the three sides of one triangle are congruent to the three sides of another triangle, then ____________.

Conjecture C-24 Conjecture C-24: SAS Congruence Conjecture If 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 protractor 2. 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 Directions Complete both sides. Show your arcs on the construction side for credit When you finished turn your quiz in at the front of the classroom. FORM A 1st picture is for #15, 2nd picture is for #16 Use this for #17. Start the h.w. pg 160 #1- 5 and #10 pg 224 #4-9, #12 – 17