Term: description named by notation (symbols) sketch an example. The intersection of two lines is a. Any determine a line.
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1 Term: description named by notation (symbols) sketch an example point line plane Collinear points Examples: Non-collinear points Examples: Coplanar: Examples: Non-coplanar: Examples: The intersection of two lines is a. Any determine a line. The intersection of two planes is a. Three determine a plane.
2 Use notation (symbols) to answer the following: 1. Give three names for the line containing point H. Is Hm an acceptable name for this line? Explain. 2. Name three coplanar points. Name the plane that they lie on. 3. Name the intersection of plane S and plane T. 4. Name the intersection of plane N and AE. 5. Name the intersection of BC 6. Does DC intersect AE? Explain. and DC. Draw and label a figure for each of the following: 7. AB is in plane Q. 8. CD intersects line n at point P. 9. EF intersects plane M at point R. 10. Point X is collinear with points G and H on plane GHJ, but point J is non-collinear. 11. Name the three line segments that intersect at point A. 12. Name the line of intersection of planes GAB and FEH.
3 Term: description named by notation (symbols) sketch an example segment length congruent segments If M is between P and Q, then. Sketch it. 1. Find GH. K is between J and L. Make a sketch and find the value of x, KL, JK, and JL. 2. JK = 6x, KL = 3x, and JL = JK = 2x, KL = x + 2, and JL = 5x 10
4 True or false? 4. AB BC 7. Find XZ. 5. ED DC 6. EF BC Simplifying radicals Perfect squares: 1 2 = 2 2 = 3 2 = 4 2 = 5 2 = 6 2 = 7 2 = 8 2 = 9 2 = 10 2 = 11 2 = 25 = 64 =
5 Distance formula Midpoint formula Find the distance to the nearest tenth between the given points. 1. A(4, 5) and B( 9, 0) 2. Find the coordinates of the midpoint of the given points. 3. A(4, 5) and B( 9, 0) M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. 6. Find the coordinates of J if K( 1, 2) is the midpoint of JL and L has coordinates (3, 5). 7. D is the midpoint of EF. EF = 4x 2, and ED = 7. Sketch a diagram. Find x, DF, and EF.
6 Segment bisector: P 9y 2 Q is the of PR. Point Q PR. Q y PQ PQ = R 8. B is between A and C. BC is three times as much as AB. AC = 84. Find BC. 9. The distance from Topeka to Kansas City, MO, is 64 miles. The distance from KC to Lawrence is five less than twice the distance from Topeka to Lawrence. Find the distance from Lawrence to KC. 10. Look back at examples 1 and 2. In what situation would it be easier to use the distance formula than the Pythagorean Theorem?
7 Term: description named by notation (symbols) sketch an example ray opposite rays angle vertex Name the vertex of this angle. Give three names for the angle. (The vertex is always the letter.) Label the interior and exterior of the angle. Name the two angles shown at right. 1 2 The width or measure of an angle is measured in. There are degrees in a circle. Right angles measure. Acute angles measure. Obtuse angles measure.
8 1. Name the vertex of Name the sides of BDC. 3. Write two other names for DBC. 4. Why is B not an acceptable name for DBC? Classify each as right, obtuse, or acute. 5. MPR 6. RPN 7. NPS Congruent angles. Angle bisector: PN bisects, therefore and. In the figure BA and BC are opposite rays. BF bisects EBC. 8. If m EBF = 6x + 4 and m CBF = 7x 2, find m EBF. 9. If m FBC = 4x and m FBA = 5x + 45, find m FBE.
9 Term: description example non-example Adjacent angles Linear pair Vertical angles Complimentary angles Supplementary angles Name an angle or angle pair that satisfies each condition. 1. two adjacent angles, one acute and one obtuse 2. two acute vertical angles 3. two supplementary adjacent angles (a.k.a. ) 4. an angle supplementary to RTS 5. two opposite rays 6. Any complimentary angles? 7. m STE =. How do you know?
10 8. Find the measures of two complimentary angles if the difference in their measures is An angle is five times the measure of its supplement. Find the measure of both angles. Perpendicular lines Symbols: AB CB Words: Segment AD is perpendicular to line CB. 10. Find the value of x and y so that NR MQ. 11. m EBF = 3x + 10, m DBE = x, and BD BF. Find the value of x. Determine whether each statement can be assumed true from the figure. 12. WZV and UZV are complimentary. 13. WZV UZV 14. YZU and UZV form a linear pair. 15. XZ UZ
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