7-2: exterior angle theorem. e xterior a ngle : an angle of a triangle that forms a linear pair with...

7-2: Exterior Angle Theorem

Upload: russell-merritt

Post on 17-Dec-2015

216 views

Category:

Documents

1 download

Report

Download

Embed Size (px):

TRANSCRIPT

7-2: Exterior Angle Theorem

EXTERIOR ANGLE: An angle of a triangle that forms a linear pair with one of the angles of the triangle.

REMOTE INTERIOR ANGLES: The angles that do not form a linear pair with the exterior angle.

Exterior AngleRemoteInteriorAngle

7-2: Exterior Angle Theorem

Identify each exterior angle.Then, identify the remote interior angles

Note that each exterior angle at a vertex share the same interior angles

Exterior Angle Remote Interior Angles

4 2 & 3

5 1 & 3

6 1 & 3

7 1 & 2

8 1 & 2

9 2 & 3

7-2: Exterior Angle Theorem

Theorem 7-3 (EXTERIOR ANGLE THEOREM): The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles. 4 = 1 + 2

Discuss Proof 41

7-2: Exterior Angle Theorem

If m2 = 38 and m4 = 134, what is m5? 4 = 2 + 5 134 = 38 + 5 96 = 5

If m2 = x + 17, m3 = 2x, and m6 = 101, find the value of x. 6 = 2 + 3 101 = x + 17 + 2x 101 = 3x + 17 84 = 3x 28 = x

7-2: Exterior Angle Theorem

Your Turn What is 1 if m3 = 46 and m5 = 96?

142 If m2 = 3x, m3 = x + 34, and m6 = 98, find the

value of x. Then, find m3. x = 16 m3 = 50

7-2: Exterior Angle Theorem

Two “common sense” theorems are derived from the Exterior Angle Theorem. Theorem 7-4: The measure of an exterior angle of a

triangle is greater than the measure of either of its two remote interior angles.

Theorem 7-5: If a triangle has one right angle, then the other two angles must be acute.

7-2: Exterior Angle Theorem

Assignment Worksheet #7-2

Day 36 Triangle Segments and Centers. Today’s Agenda Triangle Segments Perpendicular Bisector Angle Bisector Median Altitude Triangle Centers Circumcenter

Section 4.2 Angles of Triangles. The Triangle Angle-Sum Theorem can be used to determine the measure of the third angle of a triangle when the other two

Constructions - WordPress.com · Constructing a triangle given 1 side and 2 angles. (ASA) Construct triangle ABC, where AB = 11 cm, angle A = 35°, angle B = 42°. Constructing a

Table of Contents - EQUELLA · PDF fileTable of Contents CHAPTER 5: GEOMETRIC ... equilateral triangle, included angle, included side, isosceles triangle, obtuse triangle, right triangle,

Triangle Small Angle X-Ray Scattering Facility

The Triangle and Chapter 6THE TRIANGLE AND ITS PROPERTIES 119119119119119 2. Find the value of the unknown interior angle x in the following figures:6.5 ANGLE SUM PROPERTY OF A TRIANGLE

Day 3 Triangle Congruence.notebook · 2018. 8. 20. · Angle-Angle-Side (AAS) Congruence Theorem If two angles and a nonincluded side of one triangle are congruent to the corresponding

How do you find angle measurements in this triangle?

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle

Triangle AngleSum Theorem1 Jul 24 9:36 AM 3.4 Triangle Angle Theorems I CAN... Apply the Triangle Angle Sum Theorem and Exterior Angle Theorem Jul 24 9:36 AM Triangle Angle Sum Theorem

Finding the Missing Angle in a Triangle

Name: Date: Day 6: Triangle Congruence, Correspondence and ... · Angle-Side-Angle triangle congruence criteria (ASA): (Two pairs of angles and the included side are ≅) 22 Example

Sai Thao Xa Thao. Right Triangle A triangle in which one angle is equal to 90 is called right triangle. The side opposite to the right angle is

· Web viewChapter 3/4: Probability and Counting 3.1/3.2 – Triangle Sum, Exterior Angle, Exterior Angle Inequality, and Triangle inequality Theorems The Triangle Sum Theorem states:

Triangle Sum, Exterior Angle, and Exterior Angle Inequality …knightgeometry.weebly.com/uploads/8/6/9/9/86997518/5.2... · 2018-09-05 · © Carnegie Learning 5 5.2 Triangle Sum,

Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

7.1 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called

shaexams.weebly.com20 Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle,

5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°

Proving Triangles Congruentcabangonmath.com/docs/int2/unit89/int2-unit8-triangle... · 2017-02-07 · Side-Angle-Side (SAS) If two sides and the included angle of one triangle are

All Triangles= 180 degrees. Right Triangle One angle is 90 (a right angle) Right Triangle One angle is 90 (a right angle) Scalene No sides or angles

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles

The Angle Sum of a Triangle...angle sum of a triangle is 180 A B C x y z Title tdt_G_twoproofsanglesumoftriangle.pps Author AAMT Created Date 20130906071751Z

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem

Right Triangle Trigonometry - PreCalculusCoach.com...Right Triangle Trigonometry Right angle trigonometry is the trigonometry of a right-angled triangle. A right-angled triangle is

This is a right triangle: We call it a right triangle because it contains a right angle

Triangles and their properties Triangle Angle sum Theorem External Angle property Inequalities within a triangle Triangle inequality theorem Medians Altitude

f',.PRS. V L 16~· · 16. An isosceles triangle is . S . an equilateral triangle. 17. An obtuse triangle is . S . an isosceles triangle. 18. An interior angle ofa triangle and one

5.5 Inequalities in Triangles - Typepad · 5.5 Inequalities in Triangles Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater

Right Triangle Word Problems notes key - Wikispaces · PDF fileTriangle Trigonometry horizontal line horizontal line — Right Triangle Word Problems angle of elevation —Y an angle

Right Triangle Geometry - Oak Park Geometry Classes … CHAPTER 4 Right Triangle Geometry 4.1 Interior and Exterior Angles of a Triangle Triangle Sum, Exterior Angle, and Exterior

Math Tech 1 · 8-2 Finding the Missing Angle of a Triangle A TRIANGLE ANGLE SUM THEOREM: All three angles of a triangle will add up to equal 180

Triangle Theorems Notes - WPMU DEV · 2018. 2. 25. · Side-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is congruent to an angle of a second triangle, and

Warm Up Find the measure of the third angle in the triangle, given two angle measures

7.3 Proving Triangles Similar Angle-Angle Similarity (AA ~) Postulate – If two angles of one triangle are congruent to two angles of another triangle,