California Geometry: Concepts, Skills, and Problem Solving by Cindy J. Boyd

By Cindy J. Boyd

Unit 1: Geometric constitution. Unit 2: Congruence. Unit three: Similarity. Unit four: Two-and Three-Eimensional size. criteria overview. 846 pages.

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Points F and G lie in the exterior of the angle. C A B E F D G Lesson 1-4 Angle Measure 31 EXAMPLE Naming Angles You can name an angle by a single letter only when there is one angle shown at that vertex. Angles and Their Parts X a. Name all angles that have W as a vertex. W V 1 3 ∠1, ∠2, ∠3, ∠XWY, ∠ZWV, ∠YWV b. Name the sides of ∠1. 2 5 WZ and WX are the sides of ∠1. 4 Z Y c. Write another name for ∠WYZ. ∠4, ∠Y, and ∠ZYW are other names for ∠WYZ. 1. Name a pair of opposite rays. To measure an angle, you can use a protractor.

8=x Substitution Add 14 to each side. Subtract 6x from each side. Divide each side by 2. Use the value of x to find the measure of one angle. m∠ABC = 6x + 2 Given = 6(8) + 2 x=8 = 48 + 2 or 50 Simplify. Since m∠ABC = m∠DBF, m∠DBF = 50. Both ∠ABC and ∠DBF measure 50. 3. Suppose ∠JKL ∠MKN. If m∠JKL = 5x + 4 and m∠MKN = 3x + 12, find the actual measurements of the two angles. com MAKE A MODEL • Draw any ∠XYZ on patty paper or tracing paper. • Fold the paper through point Y so that YX and YZ are aligned together.

Hold the paper up to the light and fold the paper so that points A and B match exactly. Crease the paper slightly. Then open the paper. −− • Put a point where the crease intersects AB. Label this midpoint as C. • Repeat using endpoints X(-4, 3) and Y(2, 7). Label the midpoint Z. MAKE A CONJECTURE −− −− −− −− 1. What are the coordinates of point C? What are the measures of AC and CB? 2. What are the coordinates of point Z? What are the measures of XZ and ZY? 3. Study the coordinates of points A, B, and C.

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