* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 1-3 - White Plains Public Schools
Survey
Document related concepts
Algebraic geometry wikipedia , lookup
Analytic geometry wikipedia , lookup
Shape of the universe wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Line (geometry) wikipedia , lookup
History of geometry wikipedia , lookup
Transcript
1-3 Measuring and Constructing Angles Objectives SWBAT name and classify angles. SWBAT measure and construct angles and angle bisectors. HW 1.3 Page 24 {5,7,9,11,13,17,27,29,31,37} All problems must have figures redrawn into HW. Holt Geometry 1-3 Measuring and Constructing Angles Vocabulary angle vertex interior of an angle exterior of an angle measure degree acute angle Holt Geometry right angle obtuse angle straight angle congruent angles angle bisector 1-3 Measuring and Constructing Angles An angle is a formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: 1. by its vertex (a single point) 2. by a point on each ray and the vertex (3 points) 3. by a number Holt Geometry 1-3 Measuring and Constructing Angles Possible Angle Names: R, SRT, TRS, or 1 Holt Geometry 1-3 Measuring and Constructing Angles You can’t name an angle just by its vertex if there is more than one angle with that vertex. In this case, you must use all three points to name the angle, and the middle point is always the vertex. Holt Geometry 1-3 Measuring and Constructing Angles Example 1: Naming Angles Name three of the angles shown. Possible answer: BAC CAD BAD Holt Geometry 1-3 Measuring and Constructing Angles Check It Out! Example 1 Write the different ways you can name the angles in the diagram. RTQ, T, STR, 1, 2 Holt Geometry 1-3 Measuring and Constructing Angles The measure of an angle is usually given in degrees. There are 360° in a circle. Holt Geometry 1-3 Measuring and Constructing Angles How do you measure an angle? Use a protractor! Holt Geometry 1-3 Measuring and Constructing Angles Holt Geometry 1-3 Measuring and Constructing Angles Example 2: Measuring and Classifying Angles Find the measure of each angle. Then classify each as acute, right, or obtuse. A. WXV mWXV = 30° WXV is acute. B. ZXW mZXW = 130° - 30° = 100° ZXW = is obtuse. Holt Geometry 1-3 Measuring and Constructing Angles Congruent angles have the same measure. mABC = mDEF, therefore ABC DEF. This is read as “ABC is congruent to DEF.” Arc marks are used to show that the two s are . Holt Geometry 1-3 Measuring and Constructing Angles Holt Geometry 1-3 Measuring and Constructing Angles Example 3: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG Add. Post. 115 = 48 + mFEG Substitute the given values. –48° –48° 67 = mFEG Holt Geometry Subtract 48 from both sides. Simplify. 1-3 Measuring and Constructing Angles An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Holt Geometry 1-3 Measuring and Constructing Angles Example 4: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM. (4x + 6)° (7x – 12)° Holt Geometry 1-3 Measuring and Constructing Angles Check It Out! Example 4b Find the measure of each angle. JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°. Find mLJM. Step 1 Find x. LJK = KJM (–10x + 3)° = (–x + 21)° +x +x –9x + 3 = 21 –3 –3 –9x = 18 x = –2 Holt Geometry Def. of bisector Substitute the given values. Add x to both sides. Simplify. Subtract 3 from both sides. Divide both sides by –9. Simplify. 1-3 Measuring and Constructing Angles Lesson Quiz: Part I Classify each angle as acute, right, or obtuse. 1. XTS acute 2. WTU right 3. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Find mLMN. 64° Holt Geometry 1-3 Measuring and Constructing Angles Lesson Quiz: Part II 4. BD bisects ABC, mABD = , and mDBC = (y + 4)°. Find mABC. 32° 5. Use a protractor to draw an angle with a measure of 165°. Holt Geometry 1-3 Measuring and Constructing Angles Lesson Quiz: Part III 6. mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find the value of x. 35 Holt Geometry 1-3 Measuring and Constructing Angles Objectives SWBAT name and classify angles. SWBAT measure and construct angles and angle bisectors. HW 1.3 Page 24 {5,7,9,11,13,17,27,29,31,37} All problems must have figures redrawn into HW. Holt Geometry