Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Analytic geometry wikipedia , lookup
Integer triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
1-3 Measuring and Constructing Angles Objectives Name and classify angles. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Vocabulary angle vertex interior of an angle exterior of an angle measure degree acute angle Holt McDougal Geometry right angle obtuse angle straight angle congruent angles angle bisector 1-3 Measuring and Constructing Angles __________ – a figure formed by two rays, or sides, with a common endpoint called the __________ (plural: __________ ). ray vertex ray You •by •by •by can name an angle several ways: its vertex, a point on each ray and the vertex, or a number. Holt McDougal Geometry 1-3 Measuring and Constructing Angles ____________________– the set of all points between the sides of the angle. ____________________ – the set of all points outside the angle. Angle Name __________, __________ , __________ , or __________ 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. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 1 Write the different ways you can name the angles in the diagram. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 2 Find the measure of each angle. Then classify each as acute, right, or obtuse. A. WXV B. ZXW Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 2 Continued Use the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse. C. BOA D. DOB E. EOC Holt McDougal Geometry 1-3 Measuring and Constructing Angles ____________________ are angles that have the same measure. mABC = mDEF, so ABC DEF. This is read as “angle ABC is congruent to angle DEF.” __________ are used to show that the two angles are congruent. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 3a: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEG Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 3b mXWZ = 121° and mXWY = 59°. Find mYWZ. Holt McDougal Geometry 1-3 Measuring and Constructing Angles An _______________is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 4a KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 4b Find the measure of each angle. QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS. Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 4c Find the measure of each angle. JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°. Find mLJM. Holt McDougal Geometry