Congruent Triangles Can given numbers make a triangle ? Can a different triangle be formed with the same information?

Slides:

Advertisements

Similar presentations

Ambiguous Case Triangles

Advertisements

Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.

Ambiguous Case Triangles Can given numbers make a triangle ? Can a different triangle be formed with the same information?

Unit 4: Trigonometry Minds On

1 Inequalities In Two Triangles. Hinge Theorem: If two sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the.

Classifying Triangles Students will classify triangles using the lengths of the sides and the angles. S. Calahan October 2010.

Classify Triangles Standard 4C.

Ambiguous Case Triangles

5-1 Classifying Triangles

Laws of Sines. Introduction  In the last module we studied techniques for solving RIGHT triangles.  In this section and the next, you will solve OBLIQUE.

8.1.2 – Law of Sines Cont’d. SSA In the case of SSA, we have to be careful in regards to the third side – AAS or ASA is not as picky; having two angles.

Chapter 5: Trigonometric Functions Lesson: Ambiguous Case in Solving Triangles Mrs. Parziale.

Unique Triangles.

Law of Sines Lesson Working with Non-right Triangles  We wish to solve triangles which are not right triangles B A C a c b h.

Section 6.1. Law of Sines Use the Law of Sines when given: Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)

Law of Sines Lesson 6.4.

13-5 The Law of Sines Warm Up Lesson Presentation Lesson Quiz

5.5 Law of Sines. I. Law of Sines In any triangle with opposite sides a, b, and c: AB C b c a The Law of Sines is used to solve any triangle where you.

In section 9.2 we mentioned that by the SAS condition for congruence, a triangle is uniquely determined if the lengths of two sides and the measure of.

Notes Over 8.1 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles).

Sec. 5.5 Law of sines.

Law of Sines Day 2- The ambiguous case. Reminder Yesterday we talked in great detail of the 2/3 cases in which you can use law of sines: AAS ASA Today.

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

Section 4.2 – The Law of Sines. If none of the angles of a triangle is a right angle, the triangle is called oblique. An oblique triangle has either three.

Law of Sines AAS ONE SOLUTION SSA AMBIGUOUS CASE ASA ONE SOLUTION Domain error NO SOLUTION Second angle option violates triangle angle-sum theorem ONE.

Polygons and Triangles Chapter 10 Lesson 4 and 5

Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Learning Goal: I can solve word problems using Sine Law while considering the possibility of the Ambiguous.

4.5 – Prove Triangles Congruent by ASA and AAS In a polygon, the side connecting the vertices of two angles is the included side. Given two angle measures.

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.

Lesson 3.3 Classifying Triangles & Triangle Angle-Sum Theorem Do Now: Find the measure of angle and x+12 are complementary. 62+x+12 = 90 degrees.

Classifying Triangles. Two Ways to Classify Triangles  By Their Sides  By Their Angles.

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

By, Mrs. Muller.  If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent

8-5 The Law of Sines Objective: To apply the Law of Sines Essential Understanding : If you know the measures of two angles and the length of a side(AAS.

Classify the triangle by its angles and by its sides.

Isosceles Triangles.

Prove triangles congruent by ASA and AAS

Angles of Triangles.

Assignment #45 – Review for Week 10 Quiz

Triangle Congruence HL and AAS

Inequalities in two triangles

If none of the angles of a triangle is a right angle, the triangle is called oblique. All angles are acute Two acute angles, one obtuse angle.

Law of sines 6-1.

9.1 Law of Sines.

5.3 Proving Triangles are congruent:

Geometry 4.1 Triangle and Angles.

Angles of Triangles 4.2.

Objective: To apply the Law of Sines

Inequalities in Two Triangles

Triangle Congruence Shortcuts Review

[non right-angled triangles]

4-3 Triangle Congruence by ASA and AAS

Ambiguous Case Triangles

EOC Prep: Triangles.

50 a 28.1o Warm-up: Find the altitude of the triangle.

Right Triangle Definition: A triangle with one 90 degree angle.

Triangle Congruence HL and AAS

Work together to classify the triangle below using its angles and sides.

Law of Sines Notes Over If ABC is a triangle with sides a, b, c, then according to the law of sines, or.

Law of Sines AAS ONE SOLUTION SSA AMBIGUOUS CASE ASA ONE SOLUTION

Unique Triangles.

1-3 Collinearity and assumptions

Ambiguous Case Triangles

Determining if a Triangle is Possible

7.2 The Law of Sines.

Law of Sines (Lesson 5-5) The Law of Sines is an extended proportion. Each ratio in the proportion is the ratio of an angle of a triangle to the length.

The Law of Sines.

Presentation transcript:

Congruent Triangles Can given numbers make a triangle ? Can a different triangle be formed with the same information?

Conditions for Unique Triangles SSSSAS Any set of data that fits these conditions will result in one unique triangle. two shortest sides are longer than the third side two angles must sum to less than 180º AAS ASA

Ambiguous Triangle Case (aka the ‘bad’ word) This diagram is deceiving -- side-side-angle data may result in two different triangles. Side a is given but it might be possible to ‘swing’ it to either of two positions depending on the other given values. SSA A a b An acute or an obtuse triangle may be possible.