In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint.

Slides:

Advertisements

Similar presentations

Definitions and Postulates

Advertisements

1.3 Key Concepts.

Solve an equation with variables on both sides

In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint.

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint.

Standardized Test Practice

EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –( )= –625.

Solve a radical equation

1.1 Exit Ticket: Part 1 Answers

Chapter 1.3 Notes: Use Midpoint and Distance Formulas Goal: You will find lengths of segments in the coordinate plane.

 Find segment lengths using midpoints and segment bisectors  Use midpoint formula  Use distance formula.

5-Minute Check. 1.3 Use Midpoints & Distance Formulas  Students will analyze segments and determine lengths in the coordinate plane.  Why? So you can.

1.3 Use Midpoint and Distance Formulas The MIDPOINT of a segment is the point that divides the segment into two congruent segments. A SEGMENT BISECTOR.

Use Midpoint and Distance Formulas

Geometry Section1.3 Using Segments and Congruence Distance and Midpoint Formula.

Lesson 1.3 Midpoint and distance. midpoint The midpoint of a segment is the point that divides the segment into two congruent segments.

EXAMPLE 2 Rationalize denominators of fractions Simplify

EXAMPLE 3 Find a length Use the diagram to find GH. Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. SOLUTION.

Using Segments and Congruence Midpoint Formula

1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane Essential question: How do you find the distance and the.

Lesson 5 Contents Glencoe McGraw-Hill Mathematics Algebra 2005 Example 1Solve an Absolute Value Equation Example 2Write an Absolute Value Equation.

Factoring to Solve Quadratic Equations

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

EXAMPLE 3 Find side lengths SOLUTION First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Making Equations (2) Algebra 5 x + 7 Area = 53cm 2 The area of a rectangle. In each of the examples below, the area of the rectangle is given. Make an.

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Use the substitution method

ALGEBRA TILES SOLVING EQUATIONS Replace the equation with tiles: Negative Positive -X X 1.

Multiply one equation, then add

Solving Inequalities Using Addition and Subtraction

Lesson 1-3 Review Problem 1 LN means distance from point L to point N. L is located at -2 and N at 12. Subtract and take the absolute value. So, -2 – 12.

Find three cities on this map that appear to be collinear. Chicago, Bloomington, Springfield ANSWER WARM UP!

1-3 Use Midpoint and Distance Formulas Hubarth Geometry.

Rewrite a linear equation

M is the midpoint of AB. Find AM and MB. Example 1 Find Segment Lengths M is the midpoint of AB. Find AM and MB. SOLUTION AM = MB = 2 1.

Point T is the midpoint of XY . So, XT = TY = 39.9 cm.

Do now Write your comparison on the Do Now Sheet..

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve a literal equation

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

EXAMPLE 1 Evaluate powers (–5)4 = (–5) (–5) (–5) (–5) = 625 –54 = –( )

5-Minute Check.

1. Find a point between A(–3, 5) and B(7, 5).

One-Step Equations with Subtraction

Solving By Substitution

6-2 Solving Systems By Using Substitution

Solve a system of linear equation in two variables

August 29, Find a point between A(–3, 5) and B(7, 5).

Point T is the midpoint of XY . So, XT = TY = 39.9 cm.

Solve an equation by combining like terms

Find which two of the segments XY, ZY, and ZW are congruent.

Use Midpoint and Distance Formulas

3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz

EXAMPLE 1 Identify polygons

Solving One and Two Step Equations

Solving One Step Equations

1.3 Notes: Distance and Midpoints

1-2 Measuring and Constructing Segments Warm Up Lesson Presentation

Outline Collect syllabi Go over daily quiz

Solve an inequality using subtraction

Example 2B: Solving Linear Systems by Elimination

Notes Over Using Radicals

One-Step Equations with Addition and Subtraction

1.3 Use Midpoint and Distance Formulas

Presentation transcript:

In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint of XY. So, XT = TY = 39.9 cm. XY = XT + TY = = 79.8 cm Segment Addition Postulate Substitute. Add.

SOLUTION EXAMPLE 2 Use algebra with segment lengths STEP 1 Write and solve an equation. Use the fact that VM = MW. VM = MW 4x – 1 = 3x + 3 x – 1 = 3 x = 4 Write equation. Substitute. Subtract 3x from each side. Add 1 to each side. Point M is the midpoint of VW. Find the length of VM. ALGEBRA

EXAMPLE 2 Use algebra with segment lengths STEP 2 Evaluate the expression for VM when x = 4. VM = 4x – 1 = 4(4) – 1 = 15 So, the length of VM is 15. Check: Because VM = MW, the length of MW should be 15. If you evaluate the expression for MW, you should find that MW = 15. MW = 3x + 3 = 3(4) +3 = 15

GUIDED PRACTICE for Examples 1 and 2 In Exercises 1 and 2, identify the segment bisector of PQ. Then find PQ ANSWERMN;

GUIDED PRACTICE for Examples 1 and 2 2. In Exercises 1 and 2, identify the segment bisector of PQ. Then find PQ. line l ; ANSWER