Triangle Sum Properties Classify triangles and find measures of their angles. Standard:MG 2.3 Draw...
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Transcript of Triangle Sum Properties Classify triangles and find measures of their angles. Standard:MG 2.3 Draw...
Triangle Sum Properties
Classify triangles and find measures of their angles.
Standard:MG 2.3 Draw triangles from given information about them.
Student Objective: -- Students will draw triangles and solve triangle sum problems from given information about them by using equations and scoring an 80% proficiency on an exit slip.
A triangle is a polygon with three sides.
A triangle with vertices A, B, and C is called “triangle ABC” or “∆ABC.”A
CB
Classifying Triangles by Sides
A scalene triangle is a triangle with no congruent sides.
An isosceles triangle is a triangle with at least two congruent sides.
An equilateral triangle is a triangle with three congruent sides.
Classifying Triangles by Angles
•An acute triangle is a triangle with three acute angles. •A right triangle is a triangle with one right angle. •An obtuse triangle is a triangle with one obtuse angle. •An equiangular triangle is a triangle with three congruent angles.
Classification By Sides
Classification By Angles
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o.
32
1
m<1 + m<2 + m<3 = 180°
The sum of all the angles equals 180º degrees.
90º 30º
60º
60º90º30º+
180º
Property of triangles
90º 50º
40º
40º90º50º+
180º
The sum of all the angles equals 180º degrees.
Property of triangles
60º60º60º+
180º60º 60º
60º
The sum of all the angles equals 180º degrees.
Property of triangles
Ex: 1What is the missing angle?
70º70ºx+
180º70º 70º
x
180 – 140 = 40˚
90º30ºx+
180º30º 90º
x
180 – 120 = 60˚
EX: 2 What is the missing angle?
60º60ºx+
180º60º 60º
x
180 – 120 = 60˚
Ex: 3What is the missing angle?
30º78º
X+
180º78º 30º
X
180 – 108 = 72˚
EX 4:What is the missing angle?
40º40º
?+
180º40º 40º
?
180 – 80 = 100˚
What is the missing angle?
45x 10x
35x
90°, 70°, 20°
Find all the angle measures
180 = 35x + 45x + 10x
180 = 90x
2 = x
DAY 2: Triangle Sum Theorem Continued
Standard : MG 2.2 Use the properties of complementary and supplementary angles and the sum of angles of a triangle to solve problems involving an unknown angle.
Student Objective (s): -- Students will use properties of the sum of triangles and solve problems with an unknown angle from given information about them by using equations and scoring an 80% proficiency on an exit slip.
What can we find out?
The ladder is leaning on the ground at a 65º angle. At what angle is the top of the ladder touching the building?
180 = 65 + 90 + x
180 = 155 + x25˚ = x
Extention to Triangle Sum Theorem
The acute angles of a right triangle are complementary.
m A + m B = 90∠ ∠ o
The tiled staircase shown below forms a right triangle.
The measure of one acute angle in the triangle is twice the measure of the other angle.
Find the measure of each acute angle.
Find the missing angles.
Con’t
Find the missing angles.
2x + x = 90
3x = 90
x = 30˚
2x = 60˚
SOLUTION:
Find the missing angles.
2x + (x – 6) = 90˚
3x – 6 = 90
3x = 96
x = 32
2x = 2(32) = 64˚
(x – 6) = 32 – 6 = 26˚
Class workRead Lesson 4.1 “Triangle Sum” in your textbook and review the Power Point lesson again.
Homework
In your textbook:
Lesson 4.1/ 1-9, 17, 25