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Presentation transcript:

WARM UP

Unit 1 Chapter 1 1-2 Linear Measure

Unlike a line, a Line segment, or segment can be measured because it has two endpoints.

A. Find the length of AB using the ruler. Length in Metric Units A. Find the length of AB using the ruler. The ruler is marked in millimeters. Point B is closer to the 42 mm mark. Answer: AB is about 42 millimeters long. Example 1

B. Find the length of AB using the ruler. Length in Metric Units B. Find the length of AB using the ruler. Each centimeter is divided into fourths. Point B is closer to the 4.5 cm mark. Answer: AB is about 4.5 centimeters long. Example 1

Length in Standard Units Each inch is divided into sixteenths. Point E is closer to the 3-inch mark. Example 2

Length in Standard Units B. Example 2

Recall that for any two real numbers a and b, there is a real number n that is between a and b such that a < n < b. This relationship also applies to points on a line and is called betweeness of points. Concept

Find XZ. Assume that the figure is not drawn to scale. Find Measurements by Adding Find XZ. Assume that the figure is not drawn to scale. XZ is the measure of XZ. Point Y is between X and Z. XZ can be found by adding XY and YZ. ___ Example 3

Find Measurements by Adding Example 3

Find LM. Assume that the figure is not drawn to scale. Find Measurements by Subtracting Find LM. Assume that the figure is not drawn to scale. Point M is between L and N. LM + MN = LN Betweenness of points LM + 2.6 = 4 Substitution LM + 2.6 – 2.6 = 4 – 2.6 Subtract 2.6 from each side. LM = 1.4 Simplify. Example 4

Draw a figure to represent this situation. Write and Solve Equations to Find Measurements ALGEBRA Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3. Draw a figure to represent this situation. ST + TU = SU Betweenness of points 7x + 5x – 3 = 45 Substitute known values. 7x + 5x – 3 + 3 = 45 + 3 Add 3 to each side. 12x = 48 Simplify. Example 5

x = 4 Simplify. Now find ST. ST = 7x Given = 7(4) x = 4 = 28 Multiply. Write and Solve Equations to Find Measurements x = 4 Simplify. Now find ST. ST = 7x Given = 7(4) x = 4 = 28 Multiply. Answer: x = 4, ST = 28 Example 5

Concept

Congruent Segments FONTS The Arial font is often used because it is easy to read. Study the word time shown in Arial type. Each letter can be broken into individual segments. The letter T has two segments, a short horizontal segment, and a longer vertical segment. Assume that all segments overlap where they meet. Which segments are congruent? TIME Answer: The five vertical segments in the letters T, I, M, and E are congruent. The four horizontal segments in T and E are congruent. The two diagonal segments in the letter M are congruent. Example 6