What you should learn

To find the complement and supplement of an angle

To find the measure of hte third angle of a triangle given the measures of the other two angles.

NCTM Curriculm Standards 2 - 4, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Triangle

Equilateral Triangle

Congruent

Isosceles Triangle

Right Triangle

Obtuse Triangle

Acute Triangle

Introduction: On fourth down in a football game, the team with the ball usually punts. A punt is a kick in which the ball is dropped by the kicker and is kicked before it hits the ground.

The longest punt ever kicked in a college football game was kicked by Pat Brady of the University of Nevada-Reno in their 1950 game against Loyola University. The punt was 99 yards long - just 1 yard short of spanning the entire length of the football field.

How far a football will travel once it is punted depends not only on the strength of the punter, but also on the angle at which the ball is kicked. If the angle is too small, the ball will travel close to the ground, then drop; if the angle is too large, the ball will travel high, but not very far. What do you think would be the best angle at which to kick the ball?

You can use a protractor to measure angles. Your teacher will now explain further and pass out protractors.

Now look at the angle below:

Angle ABC (denoted) measures 60.04 degrees. However, where ray BC (denoted ) also shows another angle, angle DBC (denoted ). What is the sum of the measures of the two angles?

Supplementary Angles: two angles are supplementary if the sum of their measures is 180 degrees.

Exercise 1: The measure of an angle is three times the measure of its supplement . Find the measuer of each angle.

Let x = the lesser measure. Then 3x = the greater measure.

x + 3x = 180

4x = 180

(4x)/4 = 180/4

x = 45

The measures are 45 degrees and 3 * 45 = 135 degrees.

 

 

 

Complementary Angles: Two angles are complementary if the sum of their measures is 90 degrees.

Exercise 2: The backward slant of the face of a golf club is called the loft. It is designed to drive the ball in a high arc. Assuming that the angle made by the ground and the face of the club is 79 degrees, what is the measure of the loft? (The angles are complementary).

Exercise 3: The measure of an angle is 34 degrees greater than its complement. Find the measure of each angle.

A triangle is a polygon with three sides and three angles. What is the sum of the measures of the three angles of a triangle?

Sum of the Angles of a Triangle: The sum of the measures of the angles in any triangle is 180 degrees.

 

In an equilateral triangle, each angle has the same measure. We say that the angles are congruent. The sides of an equilateral triangle are also congruent. What is the measure of each angle of an equilateral triangle?

Let x = the measure of each angle

x + x + x = 180

3x = 180

(3x)/3 = 180/3

x = 60

Each angle measures 60 degrees

 

 

In an isosceles triangle, at least two angles have the same measure. Generally, the two congruent angles are the base angles.

Exercise 4: What are the measures of the base angles of an isosceles triangle in which the vertex angle measures 45 degrees?

Let x = the measure of each base angle

x + x + 45 = 180

2x + 45 = 180

2x + 45 - 45 = 180 - 45

2x = 135

(2x)/2 = 135/2

x = 135/2 = 67 1/2

The base angles each measure 67 1/2 degrees.

 

 

Triangles are often classified in one of three ways. A right triangle has one angle that measures 90 degrees. An obtuse triangle has one angle with measure greater than 90 degrees. In an acute triangle, all of the angles measure less than 90 degrees.

Exercise 5: The measures of the angles of a triangle are given as x, 2x, and 3x.

a. What are the measures of each angle?

b. Classify the triangle.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 15 - 43 odd, 44, 45, 47, 48 - 55

Alternative Homework: Enriched: 16 - 42 even, 44 - 55

Extra Practice: Students book page 763 Lesson 3-4

Extra Practice Worksheet: Click Here.

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