SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Midpoints and Segment Congruence Explained

hasad avatar
hasad
17 diapositives · 306 Views · Oct 15, 2014

Learn about midpoint formulas, segment bisectors, and theorems related to segment congruence. Practice problems and examples included.

Midpoints and Segment Congruence Explained - slide 1
01 / 17Midpoints and Segment Congruence Explained
1 / 17

Télécharger la présentation

Midpoints and Segment Congruence Explained
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Chapter 1Section 5 Midpoints: Segment Congruence

  2. Warm-Up • 1) Name two possible arrangements for G, H, and I on a segment if GH + GI = HI • 2) Use the figure below to find each measure. D A C E -10 -8 -6 -4 -2 0 2 4 6 8 10 • a)  AC • b) DE • 3) If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find MN. • 4) What is the length of ST for S(-1, -1) and T(4, 6)?

  3. 1) Name two possible arrangements for G, H, and I on a segment if GH + GI = HI •  H, G, I or I, G, H • 2) Use the figure below to find each measure. D A C E -10 -8 -6 -4 -2 0 2 4 6 8 10 • a)  AC • A= 1, C = 5 • A – C • 1 – 5 = -4 • So AC is 4. • b) DE • D = -1, E = 8 • D – E • -1 – 8 = -9 • So DE is 9.

  4. 3) If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find MN. • Use the segment addition Postulate. • LM + MN = LN • 4 + x -1 = 3x - 1 • x + 3 = 3x - 1 • 3 = 2x - 1 • 4 = 2x • 2 = x • Now plug 2 in for x in the equation for MN • MN = x - 1 • MN = 2 - 1 • MN = 1 L M N

  5. 4) What is the length of ST for S(-1, -1) and T(4, 6)? • Distance Formula • d=√((x2 – x1)2 + (y2 – y1)2) • Pick one point to be x1 and y1 and the other point will be x2 and y2. • Let point S be x1 and y1 and point T be x2 and y2. • d=√((x2 – x1)2 + (y2 – y1)2) • d=√((4 – -1)2 + (6 – -1)2) • d=√((4 + 1)2 + (6 + 1)2) • d=√((5)2 + (7)2) • d= √((25) + (49)) • d= √(74) • So the distance between the two points is √(74) or about 8.6.

  6. Vocabulary P M Q Midpoint- The midpoint M of PQ is the point between P and Q such that PM = MQ Segment bisector- Any segment, line, or plane that intersects a segment at its midpoint. Line L is a segment bisector. Theorems-A statement that must be proven. Proof- A logical argument in which each statement you make is backed up by a statement that is accepted as true. L

  7. Vocabulary Cont. Midpoint Formulas- On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is (a + b)/2. In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have the coordinates (x1, y1) and (x2, y2) are [(x1 + x2)/2, (y1 + y2)/2]. Midpoint Theorem- If M is the midpoint of line AB, then Segment AM congruent to segment MB. A M B

  8. Example 1: If the coordinate of H is -5 and the coordinate of J is 4, what is the coordinate of the midpoint of line HJ? H and J are on a number line so use the equation (a + b)/2. Let point H be a and point J be b. (a + b)/2 (-5 + 4)/2 -1/2 So the coordinate of the midpoint is at -1/2.

  9. Example 2: If the coordinate of H is -10 and the coordinate of J is 2, what is the coordinate of the midpoint of line HJ? H and J are on a number line so use the equation (a + b)/2. Let point H be a and point J be b. (a + b)/2 (-10 + 2)/2 -8/2 -4 So the coordinate of the midpoint is at -4.

  10. Example 3: Find the coordinates of the midpoint of line VW for V(3, -6) and W(7, 2). V and W are on a coordinate plane so use the equation [(x1 + x2)/2, (y1 + y2)/2]. Let point V be x1 and y1 and let point W be x2 and y2. (x1 + x2)/2 = x-coordinate of the midpoint (3 + 7)/2 10/2 5 (y1 + y2)/2 = y-coordinate of the midpoint (-6 + 2)/2 (-4)/2 -2 So the midpoint of line VW is at the point (5,-2)

  11. Example 4: Find the coordinates of the midpoint of line VW for V(4, -2) and W(8, 6). V and W are on a coordinate plane so use the equation [(x1 + x2)/2, (y1 + y2)/2]. Let point V be x1 and y1 and let point W be x2 and y2. (x1 + x2)/2 = x-coordinate of the midpoint (4 + 8)/2 12/2 6 (y1 + y2)/2 = y-coordinate of the midpoint (-2 + 6)/2 (4)/2 2 So the midpoint of line VW is at the point (6,2)

  12. Example 5: The midpoint of line RQ is P(4, -1). What are the coordinates of R if Q is at (3, -2)? R and Q are on a coordinate plane so use the equation [(x1 + x2)/2, (y1 + y2)/2]. Let point R be x1 and y1 and let point Q be x2 and y2. (x1 + x2)/2 = x-coordinate of the midpoint (x1 + 3)/2 = 4 x1 + 3 = 8 x1 = 5 (y1 + y2)/2 = y-coordinate of the midpoint (y1 + -2)/2 = -1 (y1 + -2) = -2 y1 = 0 So point R is at (5,0).

  13. Example 6: The midpoint of line RQ is P(4, -6). What are the coordinates of R if Q is at (8, -9)? R and Q are on a coordinate plane so use the equation [(x1 + x2)/2, (y1 + y2)/2]. Let point R be x1 and y1 and let point Q be x2 and y2. (x1 + x2)/2 = x-coordinate of the midpoint (x1 + 8)/2 = 4 x1 + 8 = 8 x1 = 0 (y1 + y2)/2 = y-coordinate of the midpoint (y1 + -9)/2 = -6 (y1 + -9) = -12 y1 = -3 So point R is at (0,-3).

  14. Example 7: U is the midpoint of line XY. If XY = 16x – 6 and UY = 4x + 9, find the value of x and the measure of line XY. X U Y Since U is the midpoint of line XY, we can use the midpoint formula. The midpoint formula tells us that XU is congruent or equal to UY. So XU + UY = XY; UY + UY = XY or 2(UY) = XY. 2( UY) = XY 2(4x + 9) = 16x – 6 8x + 18 = 16x – 6 18 = 8x – 6 24 = 8x 3 = x Plug 3 in for x in the equation for XY. XY = 16x – 6 XY = 16(3) – 6 XY = 48 – 6 XY = 42

  15. Example 8: U is the midpoint of line XY. If XY = 2x + 14 and UY = 4x - 5, find the value of x and the measure of line XY. X U Y Since U is the midpoint of line XY, we can use the midpoint formula. The midpoint formula tells us that XU is congruent or equal to UY. So XU + UY = XY; UY + UY = XY or 2(UY) = XY. 2( UY) = XY 2(4x - 5) = 2x + 14 8x - 10 = 2x + 14 6x - 10 = 14 6x = 24 4 = x Plug 4 in for x in the equation for XY. XY = 2x + 14 XY = 2(4) + 14 XY = 8 + 14 XY = 22

  16. Example 9: Y is the midpoint of line XZ. If XY = 2x + 11 and YZ = 4x - 5, find the value of x and the measure of line XZ. X Y Z Since Y is the midpoint of line XZ, we can use the midpoint formula. The midpoint formula tells us that XY is congruent or equal to YZ. So XY + YZ = XZ; XY + XY = XZ or 2(XY) = XZ. XY = YZ 2x + 11 = 4x - 5 11 = 2x - 5 16 = 2x 8 = x Plug 8 in for x in either of the equations. XY = 2x + 11 XY = 2(8) + 11 XY = 16 + 11 XY = 27 2(XY) = XZ 2(27) = XZ 54 = XZ

  17. Example 9: Y is the midpoint of line XZ. If XY = -3x + 9 and YZ = 4x - 5, find the value of x and the measure of line XZ. X Y Z Since Y is the midpoint of line XZ, we can use the midpoint formula. The midpoint formula tells us that XY is congruent or equal to YZ. So XY + YZ = XZ; XY + XY = XZ or 2(XY) = XZ. XY = YZ -3x + 9 = 4x - 5 9 = 7x - 5 14 = 7x 2 = x Plug 2 in for x in either of the equations. XY = -3x + 9 XY = -3(2) + 9 XY = -6 + 9 XY = 3 2(XY) = XZ 2(3) = XZ 6 = XZ