1.3 Segments and Their Measures Geometry. Postulates  Rules that are accepted as true without proof  Sometimes they are called axioms.

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Presentation transcript:

1.3 Segments and Their Measures Geometry

Postulates  Rules that are accepted as true without proof  Sometimes they are called axioms.

Postulate 1: Ruler Postulate

the measure of. Find the measure of AB. AB Point A is at 1.5 and B is at = 3.5 So, AB = = 3.5 Example 1

Example 2  Find the measure of PR  Ans: |3-(-4)|=|3+4|=7  Would it matter if I asked for the distance from R to P ?

Between

Postulate 2: Segment Addition Postulate

Example 3: DE=2, EF=5, and DE=FG. Find FG, DF, DG, & EG.

Example 4: Find the length of JT.

Ways to find the length of a segment on the coordinate plane 1) Pythagorean Theorem- Can be used on and off the coordinate plane 2) Distance Formula – only used on the coordinate plane

1) Pythagorean Theorem* * Only can be used with Right Triangles What are the parts to a RIGHT Triangle? 1. Right angle 2. 2 legs 3. Hypotenuse Right angle LEG Leg – Sides attached to the Right angle Hypotenuse- Side across from the right angle. Always the longest side of a right triangle.

Pythagorean Theorem

Example 5: Find the missing length in the triangle.  Find the missing segment- Identify the parts of the triangle 5 in 13 in Ans: X 2 = 13 2 Leg 2 + Leg 2 = Hyp 2 hyp Leg 25 + X 2 = 169 X 2 = 144 X = 12 in

Example 6: Find the distance of JT (Using the Pythagorean Theorem) Make a right Triangle out of the segment (either way) Find the length of each leg of the right Triangle. Then use the Pythagorean Theorem to find the Original segment JT (the hypotenuse).

10 8 We got 8 by | -4 – 4| We got 10 by | | Example 7: Find the distance of CD

Example 8: Observe the map to answer the following questions:

The Distance Formula

Identify one as the 1 st point and one as the 2 nd. Use the corresponding x and y values (4-(-3)) 2 + (2-(5)) 2 (4+3) 2 + (2-5) 2 (7) 2 +(-3) = 58 ~ 7.6 ~ J (-3,5) T (4,2) x 1, y 1 x 2, y 2 Example 9: Use the Distance Formula to find JT

Example 10: Use the distance formula  Find the length of the green segment Ans: 109 or approximately 10.44

Example 11: Find the lengths of all the segments. Tell whether any of the segments have the same length.

Congruent Segments