Perpendicular Lines SECTION 2.5.

Slides:



Advertisements
Similar presentations
Proofs & Perpendicular Lines Sec. 3.2 p. 136
Advertisements

Section 9.2 TANGENTS.
Proving Lines Perpendicular Page 4. To prove lines perpendicular: 12 Prove: Given: s t StatementReason 1. Given 2. Two intersecting lines that form congruent.
 Do Now: 1. Take out HW. 2. Copy down HW. 3. What are all the theorems we use to prove 2 lines are parallel?
Geometry Section 3.6 Prove Theorems About Perpendicular Lines.
HW #17 pg. 194 #5-7, 15-17, 21, 26, 29.  Theorem 3.8  If two lines intersect to form two congruent angles that are a linear pair, then the lines must.
Prove Theorems About Perpendicular Lines
Notes on Logic Continued
CHAPTER 3: PARALLEL LINES AND PLANES Section 3-1: Definitions.
6.3 Parallel Plane Facts Objectives: 1.Recognize lines parallel to planes, parallel lines and skew lines 2.Use properties relating parallel planes and.
Use right angle congruence
Ch 5.3 Use Angle bisectors of triangles. In this section… We will use the properties of an angle bisector to solve for missing side lengths.
Honors Geometry Section 4.6 (1) Conditions for Special Quadrilaterals
CHAPTER 1: Points, Lines, Planes, and Angles
Section 8.4 Special Right Triangles VERY VERY VERY VERY IMPORTANT SAT SECTION.
CHAPTER 2: DEDUCTIVE REASONING Section 2-4 A: Special Pairs of Angles.
Conjectures that lead to Theorems 2.5
2.2 Definition and Biconditional Statements Use definitions and biconditional statements.
Section 3.2 Properties of Parallel Lines. If two parallel lines are cut by a transversal, then Alternate interior angles (AIAs) are Alternate exterior.
WARM UP 1) 2). Section 9.6 Other Angles OTHER Angles in a Circle You know two types of Angles: –Central angles –Inscribed angles FOUR OTHER TYPES 1)
WARM UP Find the following measures.. Section 9.4 Relationships between Arcs and Chords.
Section 5.1 Properties of Parallelograms
Proving Angles Congruent Chapter 2 Section 6. Theorem A conjecture or statement that you can prove true. You can use given information, definitions, properties,
Section 2.5: Proving Angles Congruent Objectives: Identify angle pairs Prove and apply theorems about angles.
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.
2-5: Perpendicular Lines. Perpendicular lines: 2 lines that intersect to form right angles (90 degree angles)
Postulates and Theorems Relating Points, Lines, and Planes
Bisectors in Triangles Chapter 5 Section 3. Objective Students will identify properties of perpendicular bisectors and angle bisectors.
CONGRUENCE IN RIGHT TRIANGLES Lesson 4-6. Right Triangles  Parts of a Right Triangle:  Legs: the two sides adjacent to the right angle  Hypotenuse:
Point the Ray. Key Question: How are lines, line segments, and rays different? Learning Goals: The student will: Model and compare parallel and intersecting.
3.2 Theorems about Perpendicular Lines. Open to text p. 114 Complete the Geo-Activity.
EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB and BC are perpendicular, so by Theorem 3.9, they form.
EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right.
Lesson 1-5 Postulates and Theorems Relating
3.4 Parallel and Perpendicular Lines 1. Objectives  Understand the difference between parallel and perpendicular lines  Use the properties of parallel.
Proving the Vertical Angles Theorem (5.5.1) May 11th, 2016.
Section 2-5 Perpendicular Lines. Two lines that intersect to form right angles (90 degrees) Lines that form one right angle ALWAYS form four right angles.
2.2 Definitions and Biconditional Statements
Dot Product of Vectors.
Do Now.
2.4: Special Pairs of Angles
Deductive Reasoning 2-5 Classroom Exercises
Lesson 2-5 Perpendicular Lines (page 56)
EXAMPLE 4 Write a biconditional
Use right angle congruence
2.8 Notes: Proving Angle Relationships
3.2 Proofs and Perpendicular Lines
Angle Relationships Section 1-5.
Proof and Perpendicular Lines
Medians, Altitudes, & Perpendicular Bisectors
CHAPTER 2: DEDUCTIVE REASONING
Math Review Equations 1. Solve for x. Explain each step in a proof. Graphing Equations 2. Graph the following equation. Angle Relationships 3. Angles 1.
(The Isosceles Triangle Theorems)
3.2 Proofs and Perpendicular Lines
Six Properties of Parallelograms
2.2 Definitions and Biconditional Statements
Section 3-4 Parallel and Perpendicular lines.
Section 1-5 Postulates and Theorems Relating Points, Rays and Planes
Module 15: Lesson 5 Angle Bisectors of Triangles
Geometry Unit 3: Proofs Perpendicular Lines.
Proof and Perpendicular Lines
Exercise 4.4 Q.4 (a) Angle between ABHE and CDEH.
Section 2.2 Definitions and Biconditional Statement
(The Isosceles Triangle Theorems)
Perpendicular and Parallel Lines
(The Converse of The Pythagorean Theorem)
Congruent Triangles Section 4.2.
Planes, segments and rays can also be perpendicular to one another if they intersect at 90 degree angles.
Perpendicular and Parallel Lines
Bisectors, Medians, Altitudes
Presentation transcript:

Perpendicular Lines SECTION 2.5

Definition Perpendicular lines are two lines that intersect to form right angles (90o).

l n

Perpendicular THEOREM Perpendicular lines form adjacent angles.

2x + 10 + x – 7 = 90o 3x + 3 = 90o 3x = 87o x = 29o 2x + 10 x – 7 DRAW THIS FIRST 2x + 10

9x – 18 + 2x = 180o 11x – 18 = 180o 11x = 198o x = 18o DRAW THIS FIRST 9x – 18 2x

Name the theorem or state the definition that justifies the statement below. Definition of ⏊ ⏊ Theorem ⏊ Theorem

Now work! Written Exercises Page 58-59 #3 – 12, 18 – 25

PRACTICE PROBLEMS PAGE 57 Classroom Exercises #2-11 Line Song