Download Geometry Fall 2011 Lesson 06 _Definitions involving triangles and

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Lesson Plan #6
Class: Geometry
Date: Friday September 16th, 2011
Topic: Definitions involving triangles and line segments associated with triangles.
Aim: What are some definitions involving triangles and line segments associated with triangles?
HW #6:
Page 52 Written Exercises #’s 13-22
Objectives:
1) Students will be able to solve problems having to do with definitions involving triangles and line segments associated with
triangles
Do Now:
1) Which construction is shown in the accompanying diagram?
A) The bisector of angle ACD
B) The midpoint of line segment AC
C) The perpendicular bisector of line segment AB
D) The perpendicular bisector of line segment CD
2)
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Let’s discuss a specific type of polygon, the triangle.
A closed plane figure bounded by three or more line segments is called a polygon. The line
segments forming a polygon are called its sides. The point of intersection of two
consecutive sides of a polygon is called a vertex of the polygon. The number of vertices of
the polygon is equal to the number of sides. A line segment joining any two nonconsecutive vertices is called a diagonal. Draw a diagonal in the above polygon.
Triangles can be classified according to their sides in the following ways.
1) Scalene
2) Isosceles
3) Equilateral
What are the parts of an isosceles triangle?
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Constructing an equilateral triangle
Draw a line that is the length that you want for a side of the triangle. I have called the ends of the line
P and Q in the diagram below. Put the point of the compass at P and open the compass so that the
pencil is at Q. With this setting on the compass and the compass point at P draw an arc of a circle
above the line.
Without changing the setting on the compass move the point to Q and draw an arc which intersects the
arc you already drew.
Join P and Q to the point of intersection to form an equilateral triangle.
Assignment:
Construct an equilateral triangle with AB
A
What are some classifications of triangles based on their angles?
What are the parts of a right triangle?
What is an altitude in a triangle?
B
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Definition: An altitude of a triangle is a line segment drawn from any vertex of the triangle, perpendicular to and ending in the
line that contains the opposite side.
Sample Test Question:
Which of the figures shows an altitude of the triangle drawn?
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. none of these
Construction:
Constructing a line perpendicular to a given line through a point not on the line.
Start with two points defining the given line.
Determine the given point.
Draw an arc with its center at point 2 and a suitable radius. The arc must intersect line 1 twice at
points with a suitable distance.
Draw an arc with its center at one of the intersections of line 1 and arc 3, with a suitable radius.
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Repeat this for the other intersection. The radius must be equal to that of arc 4, and both
arcs must intersect at the opposite side of line 1 relative to point 2.
Draw the line connecting point 2 to the intersection of arcs 4 and 5.
The part of line 6 from point 2 to the intersection of it with line 1 is the line to be constructed,
perpendicular to line 1 and passing through point 2.
In Summary, your construction should look like this:
A
Assignment: Construct an altitude in the triangle at right from
point A.
B
The orthocenter of a triangle is the point where the 3 altitudes meet. This point
may be inside, outside or on the triangle. Construct the 3 altitudes in the above
triangle and identify the orthocenter.
C
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