Download Angle 1 + Angle 2 + Angle 3 = 180

Chapter 7: GEOMETRY
Section 3
TRIANGLES
California Standards
 Measurement and Geometry 2.0:
 Students identify and describe the properties of
2-dimensional figures.
 Measurement and Geometry 2.3:
 Identify angles as VERTICAL, ADJACENT,
COMPLEMENTARY, or SUPPLEMENTARY and provide
descriptions of these terms.
Key Vocabulary
 TRIANGLE: A polygon formed by three straight segments.
 SCALENE: Possessing NO sides that are EQUAL in measurement.
 ISOSCELES: Possessing 2 sides and 2 angles that are EQUAL to each other.
 EQUILATERAL: Possessing ALL sides EQUAL to each other.
 ACUTE: A term that refers to the measure of an angle.
 If an angle is ACUTE, it simply means that the angles possesses a measure
GREATER than 0° but LESS than 90°.
 RIGHT: A term that refers to an angle equaling EXACTLY 90°
 OBTUSE: A term that refers to the measure of an angle.
 If an angle is OBTUSE, it simply means that the angles possesses a measure
GREATER than 90° but LESS than 180°.
 CONGRUENT: CONGRUENT is a term that is used to describe EQUALITY.
 Here, if sides or angles are CONGRUENT, they possess the same measurement.
What is a TRIANGLE?
 A TRIANGLE is a polygon. A polygon is a closed geometric
figure made of line segments. A TRIANGLE is also known as a
TRIGON. This means its made up of 3 line segments.
 TRIANGLES are traditionally named with 3 capital letters.
These 3 lettered points are the vertices or endpoints of the
line segments.
 TRIANGLES possess 3 ANGLES and 3 SIDES.
 The TOTAL Interior Measure of a TRIANGLE is 180°.
 Basic Formula: Angle 1 + Angle 2 + Angle 3 = 180°
CLASSIFYING TRIANGLES BY SIDES
 Triangles can be classified by the MEASURE of their SIDES.
 Using identified sides or measuring tools, you can use the
measures of the sides to correctly classify a triangle.
 Once the side measures are found, TRIANGLES fall into one
of the following categories:
 SCALENE: NOT A SINGLE SIDE MEASURES THE SAME.
 ISOSCELES: A PAIR of sides is EQUAL to one another.
 EQUILATERAL: ALL 3 sides are EQUAL to each other.
CLASSIFYING TRIANGLES BY ANGLES
 Triangles can be classified by the MEASURE of their
ANGLES.
 Using identified angles or measuring tools, you can use the
measures of the angles to correctly classify a triangle.
 Once the angle measures are found, TRIANGLES fall into
one of the following categories:
 ACUTE: The measure of the ANGLES all are UNDER 90°.
 OBTUSE: The measure of one of the ANGLES is over 90°
but under 180°.
 RIGHT: The measure of one of the ANGLES is EXACTLY
90°.
MEASURES of a TRIANGLE
 The INTERIOR Measure of a Triangle ALWAYS equals
180°.
 Any combination of angle measures can be combined.
 Recall that the 3 angles will ALWAYS result in 180°.
 The BASIC FORMULA is the following:
 Angle 1 + Angle 2 + Angle 3 = 180°
 Examples: 30° + 70° + 80° = 180° (ACUTE Triangle)
45° + 45° + 90° = 180° (RIGHT Triangle)
20°+45°+115° = 180° (OBTUSE Triangle)
SOLVING FOR MISSING ANGLES
 When you are solving for the missing angle within a Triangle, you will
need to work carefully, using ALL known information and the BASIC
FORMULA. Simple Algebra will also be used to solve correctly.
 Example: There is a triangle where Angle 1 is 40° and Angle 2 is 65°.
What is the measure of Angle 3?
 Angle 1 + Angle 2 + Angle 3 = 180°
 40° + 65° + Angle 3 = 180°
 105° + Angle 3 = 180°
-105°
-105°
 Angle 3 = 75°
 40° + 65° + 75° = 180°
 180° = 180°
-Basic Formula
-Drop in Known Angles
-Known Angles are combined
-Solve Algebraically
-Result is the answer.
-Double Check
-Answer is CORRECT
Finding MORE Angles
 A Triangle exists. Angle 1 measures 85°. Angle 2 measures 25°.Please find
the measure for Angle 3.
 Angle 1+Angle 2+Angle 3=180°
 85° + 25°+ Angle 3 = 180°
 110° + Angle 3 = 180°
-110°
-110°
 Angle 3 = 70°
-Basic Formula is used
-Drop in the known Angle Measure
-Solve Algebraically
-Result is your answer
 A Triangle exists. Angle 1 measures 47°. Angle 2 measures 78°.Please find
the measure for Angle 3.
 Angle 1+Angle 2+Angle 3=180°
 47° + 78°+ Angle 3 = 180°
 125° + Angle 3 = 180°
-125°
-125°
 Angle 3 = 55°
-Basic Formula is used
-Drop in the known Angle Measure
-Solve Algebraically
-Result is your answer
QUICK REVIEW
 Classifying Triangles by SIDE Measures:
 There are 4 ways an Angle can be classified as:
 SCALENE: Not a single side is EQUAL. All are DIFFERENT Measures.
 ISOSCELES: 2 Sides are EQUAL in Measure.
 EQUILATERAL: ALL 3 sides are EQUAL in Measure.
 Classifying Triangles by ANGLE Measures:
 There are 4 ways an Angle can be classified as:
 ACUTE: Angles within the Triangle measure UNDER 90°.
 OBTUSE: One angle within the Triangle is Over 90° but Under 180°.
 RIGHT: EXACTLY 90°.
 Interior Measure of a TRIANGLE: Angle 1+Angle 2+Angle 3 = 180°
Check for Understanding
 Please determine the BEST answer for the
following expression.
 Carry out ALL work and calculations in your
NOTES for later reference
 Please write your answer on your wipe boards
and wait for the teacher’s signal.
 On the count of 3, hold up your wipe boards.
C4U Question #1
Question #1:
 A Triangle exists where a pair of sides is EQUAL in
measure. What type of Triangle is this?
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #2
Question #2:
 A Triangle exists where one of the angles is 103°
in measure, and the other two angles are 27°
and 50°. What type of Triangle is this?
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #3
Question #3:
 A Triangle exists where 2 angles are known.
Angle 1 measures 53°. Angle 2 measures 72°.
Please find the measure for Angle 3.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #4
Question #4:
 A Triangle exists where 2 angles are known.
Angle 1 measures 53°. Angle 2 measures 72°.
Please find the measure for the Angle 3.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
GUIDED PRACTICE
 Students will work on a worksheet/book work, focusing only on the
problems assigned by the teacher.
 Work carefully, show your problem solving process, and double check
all calculations.
 Use scratch paper to carry out your work.
 Once you have completed the assigned problems, please raise your
pencil.
 The teacher will then check your work and release you to complete
the independent practice.
INDEPENDENT PRACTICE
 Once you have been signed off and released to complete
Independent Practice, please complete the following assignment: