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Understanding Congruent Segments and the Distance Formula: Week 1 Warm-Up

In this lesson, we explore the concepts of congruent segments and how to apply the distance formula. We'll cover the definition of congruence in segments, demonstrate how to determine if two segments are congruent, and provide examples using coordinates to utilize the distance formula effectively. Homework will reinforce these concepts, offering practice problems and real-life applications. Engage in exercises that verify segment lengths and deepen your understanding of these foundational geometry principles.

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Understanding Congruent Segments and the Distance Formula: Week 1 Warm-Up

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  1. Week 1 Warm Up 08.18.11 1) │4 – 11│ 2) │1.2 – 4.3│ ( -2 )2 + 32 3)

  2. 19) DE + EF = DF 26) 11 Homework 1.3 Day 1 20) GH + HJ = GJ 27) 6 21) NM + MP = NP 28) 14 22) QR + RS = QS 29) 9 23) 3 30) 17 31) 4, 20 3, 23 24) 3 25) 3 32) 13, 100, 43, 143

  3. • C 21 Re 1 • A 7 AB • B AB + 7 = 21 AB = 21 - 7 AB = 14

  4. Congruent Same Congruent Segments Segments that are the same 4 4 • • A B Ex 1 • • B C Segments are Congruent Lengths are Equal AB = BC AB BC

  5. Distance Formula AB = ( x2 – x1 )2 + ( y2 – y1 )2 Ex 2 B ( 3 , 2 ) (-4 , 3 ) C A (-1 , 1 ) D ( 2 , -1 )

  6. ( x2, y2 ) ( x1, y1 ) AD = AD = AD = AD = AD = ( 3 )2 + ( -2 )2 9 + 4 13 ( x2 – x1 )2 + ( y2 – y1)2 ( 2 – ( -1 ) )2 + ( ( -1 ) – 1 )2 D( 2, -1 ) A( -1 , 1 )

  7. AC = ( x2 – x1 )2 + ( y2 – y1 )2 Do 2

  8. KL ? Ex 3 Is JK JK = JK = JK = JK = 29 ( 5 – 0 )2 + ( 2 – 0 )2 ( 5 )2 + ( 2 )2 25 + 4 J ( 0 , 0 ) K ( 5 , 2 ) L ( 8 , 6 )

  9. KL ? Is JK KL = KL = KL = KL = 25 9 + 16 ( 8 – 5 )2 + ( 6 – 2 )2 ( 3 )2 + ( 4 )2 J ( 0 , 0 ) K ( 5 , 2 ) L ( 8 , 6 ) JK and KL are not

  10. Review What is a Postulate? J ( 0 , 0 ) Is JK JL Do 3: K ( 5 , 2 ) L ( 8 , 6 ) Textbook page 22, 34 – 43 all and 46. Assignment

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