Lesson 1 Lesson 2 Lesson 3 Review
Transcript of Lesson 1 Lesson 2 Lesson 3 Review
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.)