Pre-Algebra Use the figure to name each of the following. H, I, J, and K Name a point with a capital letter. Introduction to Geometry: Points, Lines, and Planes Lesson 9-1 a. four points b. four different segments HOName a segment by its endpoints., HJ, KI, and OI IK c. five other names for KI d. five different rays, andOI, IO, OK, KO There is one line pictured. It has several names. The first letter names the endpoint of the ray.HO, OJ, KI, OK, and JH Additional Examples

Pre-Algebra MP, OP, QT, ST MQ, NR, OS MN, NO, QR, RS You are looking directly down into a wooden crate. Name each of the following. Introduction to Geometry: Points, Lines, and Planes Lesson 9-1 a. four segments that intersect PT b. three segments parallel to PT c. four segments skew to PT Additional Examples

Pre-Algebra Draw two intersecting lines. Then draw a segment that is parallel to one of the intersecting lines. Introduction to Geometry: Points, Lines, and Planes Lesson 9-1 Use the lines on notebook or graph paper. First draw two lines that intersect. Then draw a segment that is parallel to one of the lines. Additional Examples

Pre-Algebra Find the measure of 3 if m 4 = 110°. Angle Relationships and Parallel Lines Lesson 9-2 Replace m 4 with 110°.m ° = 180° Solve for m 3.m ° – 110° = 180° – 110° m 3 = 70° 3 and 4 are supplementary. m 3 + m 4 = 180° Additional Examples

Pre-Algebra 1 3, 2 4, 5 7, , 6 3 In the diagram, p || q. Identify each of the following. Angle Relationships and Parallel Lines Lesson 9-2 a. congruent corresponding angles b. congruent alternate interior angles Additional Examples

Pre-Algebra Classify the triangle by its sides and angles. Classifying Polygons Lesson 9-3 The triangle has no congruent sides and one obtuse angle. The triangle is a scalene obtuse triangle. Additional Examples

Pre-Algebra Name the types of quadrilaterals that have at least one pair of parallel sides. Classifying Polygons Lesson 9-3 All parallelograms and trapezoids have at least one pair of parallel sides. Parallelograms include rectangles, rhombuses, and squares. Additional Examples

Pre-Algebra A contractor is framing the wooden deck shown below in the shape of a regular dodecagon (12 sides). Write a formula to find the perimeter of the deck. Evaluate the formula for a side length of 3 ft. Classifying Polygons Lesson 9-3 To write a formula, let x = the length of each side. The perimeter of the regular dodecagon is x + x + x + x + x + x + x + x + x + x + x + x. Therefore a formula for the perimeter is P = 12x. P = 12xWrite the formula. = 12(3) Substitute 3 for x. = 36Simplify. For a side length of 3 ft, the perimeter is 36 ft. Additional Examples

Pre-Algebra Problem Solving Strategy: Draw a Diagram Lesson 9-4 How many diagonals does a nonagon have? AH, AG, AF, AE, AD, and AC are some of the diagonals. One strategy for solving this problem is to draw a diagram and count the diagonals. A nonagon has nine sides. You can draw six diagonals from one vertex of a nonagon. Additional Examples

Pre-Algebra Problem Solving Strategy: Draw a Diagram Lesson 9-4 (continued) A nonagon has 27 diagonals. You can organize your results as you count the diagonals. Do not count a diagonal twice. (The diagonal from A to C is the same as the one from C to A.) Then find the sum of the numbers of diagonals. VertexNumber of Diagonals A B C D E F G H I Total27 Additional Examples

Pre-Algebra V X, TW, TUVWUX TV WXWU, TUXUXU, VU Congruence Lesson 9-5 In the figure, TUV WUX. a. Name the corresponding congruent angles. b. Name the corresponding congruent sides. c. Find the length of WX. WX,TV, Since TV = 300 m, WX = 300 m.and Additional Examples

Pre-Algebra Congruence Lesson 9-5 List the congruent corresponding parts of each pair of triangles. Write a congruence statement for the triangles. ACBECDAngle ACEC Side CABCEDAngle ACBECD by ASA. a. Additional Examples

Pre-Algebra Congruence Lesson 9-5 (continued) by SAS. MKJLJK MKLJSide MKJLJK Angle JK Side b. Additional Examples