Chapter 3

Lesson 1

Lesson 2

Lesson 3

Review

Warm-Up Fill in the following statements about

quadrilaterals with ALWAYS (A), SOMETIMES (S), or NEVER (N).

1. A parallelogram is ___ a rectangle.

2. A square is ___ a rectangle.

3. A trapezoid is ___ a parallelogram.

4. A quadrilateral is ___ a kite.

5. A rhombus is ___ a square.

Reassessment

Part of Test 3: 2d and 2e

General Comments

READ DIRECTIONS!!!!!!!!!

Missing Homework = NO REASSESSMENT

Practice pages must be 100% correct before re-testing!

GET HELP IF YOU NEED IT!

Reassess the Not Proficient page

Special Segments in Triangles

line

midpoint perpendicular

The Perpendicular Bisector

Find the midpoint of side AB – label it X. Draw a 90 degree angle with X as the vertex

Find the midpoint of side BC – label it Y. Draw a 90 degree angle with Y as the vertex

Find the midpoint of side AC – label it Z. Draw a 90 degree angle with Z as the vertex

Construct your perpendicular bisectors by extending these angles until they hit the triangle somewhere else

The Perpendicular Bisector

Does a perpendicular bisector have to go through a vertex of the triangle?

The Perpendicular Bisector

On side BC, name the perpendicular bisector MY.

Draw a point, T somewhere on MY.

Measure the distance from T to B and from T to C.

Check with your tablemates what did they find?

The Perpendicular Bisector

Perpendicular Bisector Conjecture:

If there is a point on the perpendicular bisector of a segment then, it is equidistant from the endpoints of the segment.

Converse of the Perpendicular Bisector Conjecture : If any point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

Shortest Distance Conjecture:

Use your ruler to find the shortest distance from R to k.

Once you have found the shortest distance draw a segment to show that distance on the figure.

Label the point where the segment hits the line, G.

R

k

Shortest Distance Conjecture

What do you notice about the segment?

HOW DO YOU SHOW THIS WITH OUR MARKINGS?

The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.

Special Segments in Triangles

vertex

midpoint

The Median

Find the midpoint of side BC. Label it M.

Connect vertex A to M to form segment AM.

AM is a median of the triangle.

Can you draw in any other medians? How many medians does every triangle

have?

SGB has vertices S(4,7), G(6,2) and B(8,2).

Find the coordinates of point J

on GB so that SJ is a median of the triangle.

Special Segments in Triangles

vertex

line

The Altitude

Use your protractor to draw a segment from vertex A so that it hits the opposite side, BC at a right angle.

Label the point where the segment crosses BC, Y.

AY is an altitude of the triangle.

Can you draw in any other altitudes?

How many should every triangle have?

The 3 Cases of Altitude

Case I: The Acute Triangle

Case II: The Right Triangle

The 3 Cases of Altitude

Case III: The Obtuse Triangle

The 3 Cases of Altitude

Special Segments in Triangles

bisects an angle

Angle Bisectors

How can you draw an angle bisector?

Draw in angle bisectors AX, BY, and CZ.

What markings should you show?

Should you show measurements?

How many does each triangle have?

Angle Bisector Conjecture

Draw a point S on angle bisector AX.

Measure the SHORTEST distance from S to AC and from S to AB.

What is the shortest distance?

How do we mark it?

What do you notice?

Compare with your tablemates!

Angle Bisector Conjecture

Any point on the bisector of an angle is __________________ from the ___________ of the angle.

equidistant

sides

What STUCK with You?

Complete the Ticket Out the Door.

Isosceles Triangles

Draw in the four special segments on the isosceles triangles.

Median

Perpendicular Bisector

Altitude

Angle Bisector

Trace the MEDIAN picture onto patty paper and compare to the other special segments.

What do you notice?

Isosceles Triangles

In an isosceles triangle, the median drawn from the vertex angle to the base is also a(n) altitude, a(n) angle bisector, and a(n) perpendicular bisector of that triangle.

IN OTHER WORDS…all of the special segments are the same in isosceles triangles!

Almost Finished…

Take out your agenda – copy down due dates

Quiz

Test

Homework

3-1 Special Segments in Triangles #1-11

Stay in your seat until the bell rings please! (Don’t forget to push in your chair.)