Over Lesson 4–1 5-Minute Check 1 BELLRINGER: 1) Classify ΔRST. 2) Find y if ΔRST is an isosceles triangle with RS  RT.

Slides:

Advertisements

Similar presentations

Chapter 4: Congruent Triangles

Advertisements

4-2 Angles of Triangles You classified triangles by their side or angle measures. Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

4.2 Angles of Triangles.

Angles of Triangles Section 4.2.

Ch 3.4 Standard 12.0: Students find and use measures of interior and exterior angles of triangles to classify figures and solve problems. Standard 13.0.

1. If the measures of two angles of a triangle are 19º

Write and solve an equation to find the value of x.

Angles of Triangles 3-4.

Lesson 4-2 Angles of Triangles. Concept 1 Concept 2.

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.

Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

Triangles The three angles must add to 180 o. Exterior Angles.

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

Lesson 4-2 Angles of Triangles.

3.4 parallel Lines and the Triangle Angle-Sum Theorem

Concept 1. Concept 2 Example 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players.

Proving angles congruent. To prove a theorem, a “Given” list shows you what you know from the hypothesis of the theorem. You will prove the conclusion.

Preview Warm Up California Standards Lesson Presentation.

Classifying Triangles Angles of Triangles

Angles of Triangles. Objectives Find angle measures in triangles.

4.1 Apply Triangle Sum Properties. Objectives  Identify and classify triangles by angles or sides  Apply the Angle Sum Theorem  Apply the Exterior.

Angles of Triangles LESSON 4–2. Lesson Menu Five-Minute Check (over Lesson 4–1) TEKS Then/Now New Vocabulary Theorem 4.1: Triangle Angle-Sum Theorem Proof:

Lesson 1-5: Pairs of Angles

EXAMPLE 1 Classify triangles by sides and by angles Support Beams

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.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–1) Then/Now New Vocabulary Theorem 4.1: Triangle Angle-Sum Theorem Proof: Triangle Angle-Sum.

Triangles and Angles Classifying Triangles. Triangle Classification by Sides Equilateral 3 congruent sides Isosceles 2 congruent sides Scalene No congruent.

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.

Angle Relationships Lesson 9-3. Angle Relationships Vertical angles are the opposite angles formed by intersecting lines. Vertical angles are congruent.

Angles of Triangles LESSON 4–2. Over Lesson 4–1 5-Minute Check 1 A.acute B.equiangular C.obtuse D.right Classify ΔRST.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–1) Then/Now New Vocabulary Theorem 4.1: Triangle Angle-Sum Theorem Proof: Triangle Angle-Sum.

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.

Warm ups Classify ΔRST. Find y if ΔRST is an isosceles triangle with RS = RT. ___ Find x if ΔABC is an equilateral triangle.

Warm-Up Exercises Lesson 4.1, For use with pages º ANSWER right 2. 72º Classify each angle as acute, obtuse, or right. ANSWERacute.

4.2 Angles of Triangles Then: You classified triangle by their side or angle measures. Now: 1. Apply the Triangle Angle-Sum Theorem. 2. Apply the Exterior.

Splash Screen. Over Lesson 4–1 5-Minute Check 1 A.acute B.equiangular C.obtuse D.right Classify ΔRST.

1. If the measures of two angles of a triangle are 19º

Congruent Angles.

Classify each angle as acute, obtuse, or right.

4.1 Apply Triangle Sum Properties

Isosceles Triangles.

4.2 Angles of Triangles.

Table of Contents Date: 10/18 Topic: Angles of Triangles

EXAMPLE 1 Classify triangles by sides and by angles Support Beams

Lesson 4-2: Angles of Triangles

Warm Up Triangle Activity.

Angles of Triangles Section 4.2.

Classify ΔRST . A. acute B. equiangular C. obtuse D. right

Classify each angle as acute, obtuse, or right.

Agenda: Check Homework 4.2 Notes Skills Check

Class Greeting.

Measuring and Classifying Angles

Module 1- Lesson 7 and 8 Finding Unknown Angle Measures – Transversals and Auxiliary Lines Finding Unknown Angle Measures in Triangles.

LESSON 4–2 Angles of Triangles.

Base Angles & Exterior Angles

1. If the measures of two angles of a triangle are 19º

Lesson 1-5 Pairs of Angles.

Vertical Angles, Linear Pairs, Exterior Angles

Five-Minute Check (over Lesson 3) Mathematical Practices Then/Now

Geo MT 3 Lesson 1 Angle Pairs.

Five-Minute Check (over Lesson 8–2) Mathematical Practices Then/Now

Angles of Triangles Chapter 4-2 DNA.

Lesson 3-2 Isosceles Triangles.

Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices,

Presentation transcript:

Over Lesson 4–1 5-Minute Check 1 BELLRINGER: 1) Classify ΔRST. 2) Find y if ΔRST is an isosceles triangle with RS  RT.

Concept 1

Example 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. UnderstandExamine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that  1 and  2 are vertical angles.

Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side. PlanFind m  1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m  2. Then you will have enough information to find the measure of  3. Solve

Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side.  1 and  2 are congruent vertical angles. So, m  2 = 63. Answer: Therefore, m  1 = 63, m  2 = 63, and m  3 = 38. CheckThe sums of the measures of the angles in each triangle should be 180. m  = or 180 m  2 + m  = or 180

Example 1 A.95 B.75 C.57 D.85 Find the measure of  3.

Concept 3

Example 2 Use the Exterior Angle Theorem GARDENING Find the measure of  FLW in the fenced flower garden shown. m  LOW + m  OWL = m  FLWExterior Angle Theorem x + 32= 2x – 48Substitution 32= x – 48Subtract x from each side. 80= xAdd 48 to each side. Answer: So, m  FLW = 2(80) – 48 or 112.

Example 2 A.30 B.40 C.50 D.130 The piece of quilt fabric is in the shape of a right triangle. Find the measure of  ACD.

Concept 5

Example 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle. If 2  s form a linear pair, they are supplementary. Exterior Angle Theorem m  1 = Simplify. = 104 Substitution m  2 = 180 Subtract 104 from each side. 76

Example 3 Find Angle Measures in Right Triangles Subtract 132 from each side. 48 Simplify m  4 = 180 Substitution m  4 = 180 Triangle Angle-Sum Theorem (90 – 34) + m  2 + m  4 = 180 Simplify. = 42 If 2  s form a right angle, they are complementary. m  3 = 90 – 48

Example 3 Find Angle Measures in Right Triangles Subtract 131 from each side. 49 Simplify. m  = 180 Triangle Angle-Sum Theorem m  = 180 m  1 = 104, m  2 = 76, m  3 = 42, m  4 = 48, m  5 = 49

Example 3 A.50 B.45 C.85 D.130 Find m  3.