Line and Angle Relationships

Slides:



Advertisements
Similar presentations
Angles and Parallel Lines
Advertisements

Chapter 12 and Chapter 3 Geometry Terms.
Angles and Parallel Lines
Angle Relationships Vocabulary
Lesson 9.2 Angle Relationships and Parallel Lines
Geometry Lesson 1 By Lorraine Gordon Olde Towne Middle School
Introduction to Angles
GEOMETRY PRE-UNIT 4 VOCABULARY REVIEW ALL ABOUT ANGLES.
Special Pairs of Angles Lesson 8-3. Complementary Angles If the sum of the measures of two angles is exactly 90º then the angles are complementary.
Line and Angle Relationships Sec 6.1 GOALS: To learn vocabulary To identify angles and relationships of angles formed by tow parallel lines cut by a transversal.
1 Angles and Parallel Lines. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
Angle Relationships Common Necessary Vocabulary for Parallel and Intersecting Lines.
Ch. 10 Geometry: Line and Angle Relationships
Lesson 11.1 Angle and Line Relationships
Angle and Triangle Flash Cards
Transparency 1 Click the mouse button or press the Space Bar to display the answers.
Unit 1 Angles and Parallel Lines. Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
Angle Relationships.
Special Pairs of Angles Return to table of contents.
LINE AND ANGLE RELATIONSHIPS Quiz Review. TYPES OF ANGLES Acute Angles have measures less than 90°. Right Angles have measures equal to 90°. Obtuse Angles.
Angles and Parallel Lines
+ Introduction to Angles. + Introduction to Lesson The purpose of this tutorial is to introduce angles and the various relationships they have. Upon completion.
+ Angles and Lines. + What do we know about angles?
Angle Relationships Lesson 54Power Up KPage 367. Angle Relationships Adjacent angles: share a common vertex and side, but don’t over lap. Vertical (opposite)
Course 3 Points, Lines, Planes, and Angles The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.
Geometry. Definitions Geometry Definitions 1.straight angle - 180º.
7-2 Angles and Parallel Lines. Video Tutor Help Word problem: find the missing angle Relating angles and parallel linesRelating angles and parallel lines.
GEOMETRY UNIT 3 VOCABULARY ALL ABOUT ANGLES. ANGLE DEFINITION Angle A figure formed by two rays with a common endpoint.
5 minute check 1 Click the mouse button or press the Space Bar to display the answers.
Exploring Angle Pairs Unit 1 Lesson 5. Exploring Angle Pairs Students will be able to: Identify Special Angle Pairs and use their relationships to find.
Parallel Lines Cut by Transversal Created by Mrs. Bentley.
Angles and Parallel Lines
Angles and Parallel Lines
Parallel Lines & Transversals
Angle Relationships & Parallel Lines
Angles and Lines.
Topic 1-5 Angle Relationships.
Angles and Lines Final Review Part 1.
Angles and Parallel Lines
Angle Relationships.
Angle Relationship Notes
Angle Relationships.
Angle Relationships.
Exploring Angle Pairs Unit 1 Lesson 5.
Angle Relationships Teacher Twins©2014.
Parallel Lines & Angle Relationships
Angles and Parallel Lines
Parallel Lines & Transversals
Parallel Lines and Transversals
Angles and Parallel Lines
Angles and Parallel Lines
Angles and Parallel Lines
Angles and Parallel Lines
Angles and Parallel Lines
Angles and Parallel Lines
Angle Relationships By Trudy Robertson.
Angles on Lines and Figures Vocabulary
TRANSVERSAL VOCABULARY
Angles and Parallel Lines
Objectives: Identify parallel and perpendicular lines
3.1 Parallel lines and transversals
TRANSVERSAL VOCABULARY
Angles and Parallel Lines
Angles and Parallel Lines
Warmup! Use the figure at right to: 1. Name the set of parallel lines.
Angles and Parallel Lines
Angle Relationships Teacher Twins©2014.
Parallel Lines & Transversals
Parallel Lines & Transversals
Presentation transcript:

Line and Angle Relationships Lesson 6-1 Line and Angle Relationships

Definitions Acute Angles – Angles with measures less than 90°. Right Angles - Angles with a measure of 90. Obtuse Angles - Angles with measures between 90° and 180°. Straight Angles – Angles with measures equal to 180.

Vertical Angles are opposite angles formed by intersecting lines Vertical Angles are opposite angles formed by intersecting lines. They are congruent. Adjacent Angles have the same vertex, share a common side, and do not overlap. The sum of the measures of complementary angles is 90°. The sum of the measures of supplementary angles is 180°

Examples 1 and 2 Classify each angle or angle pair using all names that apply. 1 m ∠1 is greater than 90°. So, ∠1 is an obtuse angle. Ex. 1 ∠1 and ∠2 are adjacent angles since they have the same vertex, share a common side, and do not overlap. 1 2 Ex. 2 Together they form a straight angle measuring 180°. So, ∠1 and ∠2 are also supplementary angles.

Classify each angle or angle pair using all names that apply. b. 60° 30° a. c. 3 4

Example 3 In the figure m∠ABC = 90°. Find the value of x. x° 65° A B C m∠ABD + m∠DBC = 90° x + 65 = 90 - 65= -65 x = 25

Find the value of x in each figure. 38° d. e. x° 150°

Definitions Lines that intersect at right angles are called perpendicular lines. Two lines in a plane that never intersect or cross are called parallel lines. p q Symbol: p q Symbol: m ⟘ n m n

Definitions A line that intersects two or more other lines is called a transversal. When a transversal intersects two lines, eight angles are formed that have special names. If two lines cut by a transversal are parallel, then these special pairs of angles are congruent. transversal 1 2 4 3 5 6 7 8

Definitions Alernate Inerior Angles – Those on opposite sides of the transversal and inside the other two lines are congruent. Ex. ∠2 ≅ ∠8 Alternate Exterior Angles – Those on opposite sides of the transversal and outside the other two lines, are congruent. Ex. ∠4 ≅ ∠6 Corresponding Angles - Those in the same position on the two lines in relation to the transversal, are congruent. Ex. ∠3 ≅ ∠7 1 2 4 3 5 6 7 8

Example 4 You are building a bench for a picnic table. The top of the bench will be parallel to the ground. If m∠1 = 148°, find m∠2 and m∠3. 3 2 1 Since ∠1 and ∠2 are alternate interior angles, they are congruent. So, m∠2 = 148°. Since ∠2 and ∠3 are supplementary, the sum of their measures is 180°. Therefore, m∠3 = 180° - 148° or 32°.