NAME DATE PERIOD. An angle is formed by two rays that share a common endpoint called the.

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1 Lesson 1 Classify Angles An angle is formed by two rays that share a common endpoint called the. An angle can be named in several ways. The symbol for angle is Angles are classified according to their measures. Two angles that have the same measure are said to be. Two angles are if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent. Two angles are if they share a common vertex, a common side, and do not overlap. Example Name each angle below. Then classify the angle as acute, right, obtuse, or straight What is the value of x in the figure at the right?

2 Exercises Name each angle. Then classify the angle as acute, right, obtuse, or straight Find the value of x in the figure at the right.

3 Lesson 1 Homework Practice Classify Angles Use the figure at the right to answer Exercises Name two angles that are vertical. 2. Name two angles that are adjacent. 3. Find the value of x. 4. Find the value of y. Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight

4 Lesson 1 Classify Angles An angle is formed by two rays that share a common endpoint called the vertex. An angle can be named in several ways. The symbol for angle is. Angles are classified according to their measures. Two angles that have the same measure are said to be congruent. Two angles are vertical if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent. Two angles are adjacent if they share a common vertex, a common side, and do not overlap. Example Name each angle below. Then classify the angle as acute, right, obtuse, or straight Use the vertex as the middle letter and a point from each side, ABC, CBA, or use the vertex or the number only, B or 1. The angle is 90, so it is a right angle. Use the vertex or the number only, D or 2. The angle is less than 90, so it is an acute angle. 3. What is the value of x in the figure at the right? The angle labeled 5x and the angle labeled 55 are vertical angles. Since vertical angles are congruent, the value of x is 11.

5 Lesson 2 Complementary and Supplementary Angles Two angles are complementary if the sum of their measures is. Two angles are supplementary if the sum of their measures is. Examples Identify each pair of angles as complementary, supplementary, or neither Example 3 ALGEBRA Find the value of x.

6 Exercises Identify each pair of angles as complementary, supplementary, or neither ALGEBRA Find the value of x in each figure

7 Lesson 2 Homework Practice Complementary and Supplementary Angles Classify each pair of angles as complementary, supplementary, or neither ALGEBRA Find the value of x in each figure

8 Lesson 2 Complementary and Supplementary Angles Two angles are complementary if the sum of their measures is 90. Two angles are supplementary if the sum of their measures is 180. Examples Identify each pair of angles as complementary, supplementary, or neither = = 90 The angles are supplementary. The angles are complementary. Example 3 ALGEBRA Find the value of x. Since the two angles form a straight line, they are supplementary. The sum of their measures is x + 35 = 180 Write the equation. 35 = 35 Subtract 35 from each side. 5x = Divide each side by 5 x = 29 Simplify.

9 Lesson 3 Triangles Every triangle can be classified by its angles and sides. Classify Triangles Using Angles all acute angles (less than 90 ) 1 right angle 1 obtuse angle (greater than 90 ) triangle triangle triangle Classify Triangles Using Sides no congruent sides at least 2 congruent sides 3 congruent sides triangle triangle triangle Example The figure shows a triangular pennant tied to a pole. Classify the marked triangle by its angles and by its sides. The sum of all the angles of a triangle equals 180 Ex. 2 Find the measure of x to in the triangle to the right.

10 Examples: Find the value of x Find the missing measure in each triangle with the given angle measures , 35.8, x Classify the marked triangle in each object by its angles and by its sides. 4.

11 Lesson 3 Homework Practice Triangles Find the value of x Find the missing measure in each triangle with the given angle measures , x, 40 Classify the marked triangle in each object by its angles and by its sides. 4.

12 Lesson 3 Triangles Every triangle has at least two acute angles. One way you can classify a triangle is by using the third angle. Another way to classify triangles is by their sides. Sides with the same length are congruent segments. Classify Triangles Using Angles all acute angles 1 right angle 1 obtuse angle acute triangle right triangle obtuse triangle Classify Triangles Using Sides no congruent sides at least 2 congruent sides 3 congruent sides scalene triangle isosceles triangle equilateral triangle Example The figure shows a triangular pennant tied to a pole. Classify the marked triangle by its angles and by its sides. The triangle has three acute angles and two sides the same length. So, it is an acute, isosceles triangle.

13 Lesson 4 Scale Drawings A represents something that is too large or too small to be drawn or built at actual size. The gives the relationship between the drawing/model measure and the actual measure. To figure out a model or actual distance, set up a proportion. Example On this map, each grid unit represents 50 yards. Find the horizontal distance from Patrick s Point to Agate Beach. Patrick s Point Exercises Find the actual distance between each pair of cities. Round to the nearest tenth if necessary. Cities 1. Los Angeles and San Diego, CA 2. Lexington and Louisville, KY 3. Des Moines and Cedar Rapids, IA 4. Miami and Jacksonville, FL Map Distance Scale 6.35 cm 1 cm = 20 mi 15.6 cm 1 cm = 5 mi cm 2 cm = 15 mi cm! " cm = 20 mi Actual Distance

14 Find the length of each object on the scale drawing with the given scale. Then find the scale factor. 5. an automobile 16 feet long; 1 inch:6 feet 6. a pond 85 feet across; 1 inch = 4 feet 7. a parking lot 200 meters wide; 1 centimeter:25 meters 8. a flag 5 feet wide; 2 inches = 1 foot

15 Lesson 4 Homework Practice Scale Drawings Find the length of each model. Then find the scale factor SKYSCRAPER A model of a skyscraper is made using a scale of 1 inch:75 feet. What is the height of the actual building if the height of the model is 19 inches?

16 Lesson 4 Scale Drawings A scale drawing/model represents something that is too large or too small to be drawn or built at actual size. The scale gives the relationship between the drawing/model measure and the actual measure. Example On this map, each grid unit represents 50 yards. Find the horizontal distance from Patrick s Point to Agate Beach. Scale map! $%&' = 0 $%&'. actual () *+,-. 1 *+,-. Patrick s Point to Agate Beach map actual 1 x = 50 8 Cross products x = 400 Simplify. It is 400 yards from Patrick s Point to Agate Beach

17 Lesson 5 Draw Three-Dimensional Figures A solid is a three dimensional figure. Example 1 Draw a top, a side, and a front view of the solid at the right. The top view is a triangle. The side and front views are rectangles. Example 2 Draw the corner view using the top, side, and front views shown below.

18 Exercises 1. Draw a top, a side, and front view of the solid. 2. Draw a corner view of the three-dimensional figure whose top, side, and front views are shown. Use isometric dot paper.

19 Lesson 5 Homework Practice Draw Three-Dimensional Figure Draw a top, a side, and a front view of each solid

20 Lesson 5 Draw Three-Dimensional Figures A solid is a three dimensional figure. Example 1 Draw a top, a side, and a front view of the solid at the right. The top view is a triangle. The side and front views are rectangles. Example 2 Draw the corner view using the top, side, and front views shown below. Step 1 Use the top view to draw the base of the figure, a 1-by-3 rectangle. Step 2 Add edges to make the base a solid figure. Step 3 Use the side and front views to complete the figure.