Triangle Sum Property Theorem

Slides:

Advertisements

Similar presentations

4.2 Angles of Triangles Objectives: *Apply the Angle Sum Theorem.

Advertisements

Warm Up Simplify the following: 3(-4m + 8) -6(2m – 4) + 10 Solve and graph the solution set for the following inequalities y + 5 ≤ 3 w + 6 < -5 The support.

4-2 Angles of Triangles Objectives: The student will be able to: 1. Apply the Triangle-Sum Theorem. 2. Apply the Exterior Angle Theorem.

HOW TO FIND AN ANGLE MEASURE FOR A TRIANGLE WITH AN EXTENDED SIDE

Classify Triangles Standard 4C.

4.1 – Apply Triangle Sum Properties

Triangles 11.2.

5-6 Inequalities in One Triangle

Triangle Angle Sum. Properties of triangles Triangles have three sides and three angles Triangles are named according to their vertices The sum of the.

Triangle Sum Properties & Inequalities in a Triangle Sections 4.1, 5.1, & 5.5.

Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180°

5.5Use Inequalities in a Triangle Theorem 5.10: If one side of a triangle is longer than the other side, then the angle opposite the longest side is _______.

5.6 Inequalities in One Triangle The angles and sides of a triangle have special relationships that involve inequalities. Comparison Property of Inequality.

Angles of Triangles Chapter 4, Section 2. Angle Sum Theorem The sum of angles in a triangle is 180 o

ANGLES OF A TRIANGLE Section 4.2. Angles of a Triangle Interior angles  Original three angles of a triangle Exterior angles  Angles that are adjacent.

Classify triangles by sides No congruent sides Scalene triangle At least two sides congruent Isosceles triangle Three congruent sides Equilateral triangle.

4.7 Triangle Inequalities. In any triangle…  The LARGEST SIDE lies opposite the LARGEST ANGLE.  The SMALLEST SIDE lies opposite the SMALLEST ANGLE.

I can use theorems, postulates and/or definitions to prove theorems about triangles including: measures of interior angles of a triangle sum to 180 degrees.

Triangle Sum Properties

Lesson 5.2 Polygon Exterior Angle Sum HOMEWORK: 5.2/ 1-10.

Geometry Triangles. Vocabulary  Theorem 4-1 (angle sum theorem): The sum of the measures of the angles of a triangle is 180 In order to prove the angle.

Write a statement about the sum of the interior angles of a triangle below: The sum of all the interior angle in a triangle is 180 o

1 Triangle Inequalities. 2 Triangle Inequality The smallest side is across from the smallest angle. The largest angle is across from the largest side.

Chapter 5.5 Inequalities in Triangles. Property: Comparison Property of Inequality If a = b+c and c > 0, then a > b Proof of the comparison property –

Angles of Triangles Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 degrees. Third Angle Theorem If two angles of one triangle.

3.4.  The sum of the measures of the angles of a triangle is 180.

Triangles The sum of the measures of the angles of a triangle is 180 degrees. m A + m B + m C = 180 o A BC An angle formed by a side and an extension.

+ Angle Relationships in Triangles Geometry Farris 2015.

3-5 Parallel Lines and Triangles I can apply the triangle angle sum theorem to find the values of variables. I can apply the exterior angle theorem to.

4.1 Triangle Angle Sum and Properties. How many degrees in a triangle? The sum of the angles in any triangle is exactly 180 degrees.

Isosceles Triangles.

Angles of Triangles.

Measuring Angles in Triangles

Angles in a Triangle By Shirley Sides 2006.

Geometry 4.1 Triangle and Angles.

3.5 Parallel lines and Triangles

Angles of Triangles 4.2.

Exterior Angles of Triangles

7-4 Triangle Inequality Theorem

Angle Relationships & Parallel Lines

Triangle Application Theorems

Lesson 5-3 Triangles Obj: I can find unknown angles and identify possible side lengths in triangles HWK: p all, all Vocab: 1) Triangle Sum.

Triangle Inequalities

Warm-up Find x a) b).

Exterior Angles of Triangles

Triangle Inequalities

Lesson 5-3 Triangles Obj: The student will be able to find unknown angles and identify possible side lengths in triangles HWK: p all, all.

Triangle Theorems.

Lesson 5-3 Triangles Obj: I can find unknown angles and identify possible side lengths in triangles HWK: p all, all Vocab: 1) Triangle Sum.

Use Inequalities in a Triangle

TRIANGLE INEQUALITY THEOREM

Base Angles & Exterior Angles

Identify type of triangle

Triangles 7.G.2 Focus on knowing the properties of triangles from three measures of angles or sides, noticing when the conditions determine a unique.

Drill 1) x = 180, solve for x 2) How many degrees do the interior angles of a triangle add up to. 3) What type of triangle has an angle that.

Triangle sum property.

Exterior Angles in a Triangle

Side – Angle Inequalities

Exterior Angle Theorem

Side – Angle Inequalities

1-3 Collinearity and assumptions

Triangle Inequalities

Determining if a Triangle is Possible

Prove that the interior angles of a triangle have a sum of 180º

Lesson 3-2 Isosceles Triangles.

Inequalities in Two Triangles

Presentation transcript:

Triangle Sum Property Theorem The sum of the measures of the interior angles of a triangle is 180o. 3 2 1 ∠1 + ∠2 + ∠3 = 180°

The sum of the measures of the interior angles of a triangle is 180o. Property of triangles The sum of the measures of the interior angles of a triangle is 180o. 60º 90º 30º + 60º 180º 30º 90º

The sum of the measures of the interior angles of a triangle is 180o. Property of triangles The sum of the measures of the interior angles of a triangle is 180o. 60º 60º 60º 60º + 180º 60º 60º

Example: Can 100°,120°be any two angles of a triangle? Solution : Sum of the given angles is 100°+120°= 220°. This is greater than 180°, but the sum of the measures of the angles of a triangle should always be 180°. Even though the third angle is not known it is not possible to form a triangle with the given measures. Therefore a triangle cannot have two obtuse angles.

Can we draw a triangle using the given angles? 80O , 60O , 70O Try These: Can we draw a triangle using the given angles? 80O , 60O , 70O 45O , 55O , 80O