4-1 Detour Proofs Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown.

Slides:

Advertisements

Similar presentations

Detour Proofs and Midpoints

Advertisements

4.1 Detours & Midpoints Obj: Use detours in proofs Apply the midpoint formulas Apply the midpoint formulas.

The Midpoint of a Line Segment We are going to elevate our study in analytic geometry past slope and intercepts. This will allow us to model more complex.

Objective: Determine if triangles in a coordinate plane are similar. What do we know about similar figures? (1)Angles are congruent (2)Sides are proportional.

ADVANCED GEOMETRY 3.1/2 What are Congruent Figures? / Three ways to prove Triangles Congruent. Learner Objective: I will identify the corresponding congruent.

4-3 A Right Angle Theorem Learner Objective: Students will apply a Right Angle Theorem as a way of proving that two angles are right angles and to solve.

Distance, Midpoint, & Slope. The Distance Formula Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2, y 2 = 1 d = Example:

Today – Wednesday, January 16, 2013  Learning Target: Review Ch.5 by practicing Ch.5 concepts in text book  Review Content from each chapter.

ADVANCED GEOMETRY 3.6 Types of Triangles LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs.

Distance, Slope, and Midpoint Day 10. Day 10 Math Review.

Lesson 1-3 Formulas Lesson 1-3: Formulas.

Proving the Midsegment of a Triangle Adapted from Walch Education.

Distance and midpoint.

1-7: Midpoint and Distance in the Coordinate Plane

You have used coordinate geometry to find the midpoint of a line segment and to find the distance between two points. Coordinate geometry can also be used.

Warm Up Evaluate. 1. Find the midpoint between (0, 2x) and (2y, 2z).

Chapter 4 Lines in the Plane

Use Midpoint and Distance Formulas

COORDINATE GEOMETRY PROOFS USE OF FORMULAS TO PROVE STATEMENTS ARE TRUE/NOT TRUE: Distance: d= Midpoint: midpoint= ( ) Slope: m =

Objective: After studying this lesson you will be able to use detours in proofs and apply the midpoint formula. 4.1 Detours and Midpoints.

Geometry Vocabulary 2.7 Substitution Property: When pairs of angles or segments are congruent to each other, one may be substituted into any statement.

Midpoint and Distance Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the Distance Between Two Points on a Coordinate Plane 12.6.

Proof using distance, midpoint, and slope

Tests for Parallelograms Advanced Geometry Polygons Lesson 3.

DISTANCE AND MIDPOINT. DISTANCE  Given any two points on a coordinate plane you can find the distance between the two points using the distance formula.

Midpoint and Distance Formulas Section 1.3. Definition O The midpoint of a segment is the point that divides the segment into two congruent segments.

Isosceles Triangles & Coordinate Proof

 Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side  Theorem 5.1  Any point.

Prove Theorems Advanced Geometry Deductive Reasoning Lesson 4.

Using Coordinate Geometry to Prove Parallelograms

UNIT 7 LESSON 4B PROVING PARALLELOGRAMS CCSS G-CO 11: Prove theorems about parallelograms. LESSON GOALS Use properties of parallelograms to prove that.

The Distance and Midpoint Formulas Unit 8. Warm – Up!! As you walk in, please pick up your calculator and begin working on your warm – up!! 1. Use the.

Midpoint and Distance Formulas

Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4.

April 17, 2012 Midpoint and Distance Formulas

Proof that the medians of any triangle meet at one point. Proof #2 Using algebra and analytic geometry.

Slope & Midpoint on the Coordinate Plane. SLOPE FORMULA Given two points (x 1,y 1 ) and (x 2,y 2 ) SLOPE The rate of change to get from one point to another.

Midpoint Objective: Students will be able to apply the midpoint formula to find endpoints and midpoints of segments.

Midpoint and Distance Formulas

Distance and Midpoint in the Coordinate Plane

Midpoint and Distance Formulas

1-7: Midpoint and Distance in the Coordinate Plane

Midpoint Formula & Partitions

Midpoint and Distance Formulas

Midpoint and Distance in the Coordinate Plane

Distance and Midpoint in the Coordinate Plane

Distance and Midpoint Formulas

Coordinate Geometry Notes Name:____________________________

Unit 5 Lesson 4.7 Triangles and Coordinate Proofs

Obj: Use detours in proofs Apply the midpoint formulas

7-3 Triangle Similarity: AA, SSS, SAS

Notes #3 (1.3) 1-3 Distance and Midpoints

12/1/2018 Lesson 1-3 Formulas Lesson 1-3: Formulas.

Unit 5: Geometric and Algebraic Connections

Midpoint in the Coordinate Plane

4.1 Detours and Midpoints Objective:

What theorems apply to isosceles and equilateral triangles?

Proving a quadrilateral is a parallelogram

Review Unit 6 Test 1.

Lesson 8.3 (part 1) Slope.

CPCTC and Circles Advanced Geometry 3.3.

Warm Up Construct a segment AB.

Unit 1 Test Review.

GEOMETRY Section 4.7 Intro to Coordinate Proofs

BELLWORK Find the midpoint between the following pairs of points.

3.5 Overlapping Triangles

Advanced Geometry Section 3.8 The HL Postulate

Section 1.5 – Division of Segments and Angles

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

4-2 The Case of the Missing Diagram

Presentation transcript:

4-1 Detour Proofs Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Advanced Geometry

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. A B C D E F G Warm-Up Given: Prove: STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. The Midpoint Formula If A = and B =, then the midpoint M = of can be found by using the midpoint formula: A B M

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Note the difference between Slope and Midpoint: Slope is the ratio of rise to run. Thus the answer to a slope question is a ratio (fraction). Slope is calculated using the formula: The Midpoint is a Point. Thus the answer to a Midpoint question is an ordered pair that gives the x and y coordinates of that point. The x coordinate of the midpoint is the AVERAGE of the x coordinates of the segment's endpoints and the y coordinate of the midpoint is the AVERAGE of the y coordinates of the segment's endpoints.

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Example: Find the Slope and the Midpoint of the segment having endpoints at (-4, 1) and (8, 7). Slope Midpoint

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

Assignment 4.1: 1-9

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS