1. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 1-3 Measuring and Constructing Angles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

2. 1-3 Measuring and Constructing Angles 31 4 Warm Up 1.Draw AB and AC, where A, B, and C are noncollinear. 2. Draw opposite rays DE and DF. Solve each equation. 3. 2x + 3 + x – 4 + 3x – 5 = 180 4. 5x + 2 = 8x – 10 E F D C B A Possible answer:

3. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Name and classify angles. Measure and construct angles and angle bisectors. Objectives

4. Holt McDougal Geometry 1-3 Measuring and Constructing Angles An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number. There are four ways to name this angle. 1.

5. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 2. You cannot name an angle just by its vertex if the point is the vertex of more than one angle. In this case, you must use all three points to name the angle, and the middle point is always the vertex. A B C D Which angle am I talking about? Hmmm… We have no clue! This is why you CAN’T name an angle by 1 letter if there’s a lot going on E

6. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 3. How many different ways can we name all of the following angles?

7. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 4. The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle.

8. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 5. The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is of a circle.

9. Holt McDougal Geometry 1-3 Measuring and Constructing Angles

10. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Congruent angles are angles that have the same measure. In the diagram, so you can write. This is read as “ angle ABC is congruent to angle DEF. ” Arc marks are used to show that the two angles are congruent. I call them “swoops.” 6)

11. Holt McDougal Geometry 1-3 Measuring and Constructing Angles

12. Holt McDougal Geometry 1-3 Measuring and Constructing Angles 7. An angle bisector is a ray that divides an angle into two congruent angles. JK bisects ; thus. *K is in the interior of <LJM

13. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 8 KM bisects, and Find. m<JKM = m<MKL (4x + 6)° = (7x – 12)° +12 4x + 18 = 7x –4x 18 = 3x 6 = x

14. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Check It Out! Example 4a Find the measure of each angle. QS bisects ∠ PQR, m ∠ PQS = (5y – 1)°, and m ∠ PQR = (8y + 12)°. Find m ∠ PQS. 5y – 1 = 4y + 6 y – 1 = 6 y = 7 Step 1 Find y. Step 2 Find m ∠ PQS. m ∠ PQS = 5y – 1 = 5(7) – 1 = 34