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Detailed review and practice problems covering factorization, vocabulary definitions, point collinearity, plane intersection, line segments, angle properties, distance, and midpoint calculations.
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Make sure you know how to: • Factor to solve word problems • Define and draw examples of any vocabulary words • Explain in words why you did what you did
Lesson 1 E A B • How many planes are in the figure? Name all planes in the figure • Name 3 collinear points. Explain how you know they are collinear • Name 4 non-coplanar points. Explain. • Name a line that intersects plane Y G F D Y C
Lesson 2 Find a if AB = 4a + 10, BC = 3a – 5, and AC = 19. C. Find x and SU if T is between S and U, ST = 7x, TU = 42, and TU = 5x – 3.
Lesson 3 • Given the ordered pairs, find the distance and midpoint • A(1, 4) B(3, 6) • A(-5, -3) B(-7, -3) • Use the number line for each question • Find the distance for AH and DB • Find the midpoint for CE and GA A B C D E F G H -5 0 5
Lessons 4 & 5 C B A D G • Name a pair of obtuse vertical angles • Name a pair of acute vertical angles • Name a pair of supplementary angles • Name a pair of complementary angles • If angle AGF= 3x-8 and angle CGD=x+24, find x and the measure of angle AGF • If angle BGD=3a+33 find a • If ray GC is an angle bisector then what is the measure of angle BGC? E F
More Lessons 4 & 5 • If two angles are supplementary and the measure of one angle is 5 more than 4 times the other, what are the measures of the angles? • If angles 1 & 2 are complementary and angle 2 is 10 more than 3 times angle 1, what is the measure of each • If two angles form a linear pair and they are congruent then what are the measures of the angles? • If two angles are supplementary and one angle is equal to half the other angle plus 18, what are the measures of the angles?
Answers • Slide 1 • 4 planes: Planes Y or FGD, EGD, EGF, and EFD • Points A, B, C are collinear because the all share the same line • Points A, G, D, and E (or A or C) are non-coplanar because E is not in the plane with A, G, and D. • Line AC
Answers • Slide 2 • a = 2 • x = 9, SU = 105
Answers • Slide 3 • (2, 5) • 2 (-6, -3) • AH = 16 DB = 5 • Mdpt of CE = 0 mdpt of GA = -3/2
Answers • Slide 4 • Angles AGC and FGD • Angles AGF and CGD • Angles AGF and FGD/AGC Angles AGB and BGD Angles CGD and ACG/DGF • Angles BGC and CGD • 3x-8=x+24, x=16, angle AGF=40 • 45 degrees each
Answers • Slide 5 • 5+4x+x=180 5+5x=180, x= 35, angles= 35 and 145 • X+3x+10= 90 4x+10=90, x=20, angles = 20 and 70 • 90 degrees each • x+ 1/2x +18=180 3/2x +18=180, x=108, angles = 108 and 72