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Transcript

CHAPTER 1 1-3 MEASURING AND CONSTRUCTING ANGLES DEFINITIONS • What is an angle? • It is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). How can we name an angle? You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number. HOW TO NAME AN ANGLE • 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. • Examples of naming angles can be: Angle Name R, SRT, TRS, or 1 EXAMPLE 1 • A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. • Answer:BAC, CAD, BAD EXAMPLE 2 Name the following angles in three different ways 1-3 MEASURING AND CONSTRUCTING ANGLES USING A PROTRACTOR • You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor. • If OC corresponds with c and OD corresponds with d, • mDOC = |d – c| or |c – d|. EXAMPLE 3 • Find the measure of each angle. Then classify each as acute, right, or obtuse. • A. WXV • mWXV =180-150= 30° • WXV is acute. B. ZXW mZXW = |130° - 30°| = 100 ZXW = is obtuse EXAMPLE 4 • What are congruent angles? Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent. ANGLE ADDITION POSTULATE EXAMPLE 5 What is m<TSW if m<RST = 50 and m<RSW = 125? T x W 50 R S Step 1: Set up an equation RST TSW RSW Step 2: Plug in the given information Step 3: Solve for the missing variable. 50 x 125 x 75 ASSIGNMENT #6 • • • • Pg. 24 #2-8 even #12-16 even #33 EXAMPLE 6 • T is in the interior of RSU . Find the following: • A) mRSU if mRST is 12 and mTSU is14.5 • B) mRST ifmTSU is 10.3 and mRSU is 65 ANGLE BISECTOR • What is an angle bisector ? • An angle bisector is a ray that divides an angle into two congruent angles. • JK bisects LJM; thus LJK KJM. Example 7: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM. Example 7 Continued Step 1 Find x. mJKM = mMKL Def. of bisector (4x + 6)° = (7x – 12)° +12 +12 Substitute the given values. Add 12 to both sides. 4x + 18 –4x = 7x –4x 18 = 3x 6=x Simplify. Subtract 4x from both sides. Divide both sides by 3. Simplify. Example 7 Continued Step 2 Find mJKM. mJKM = 4x + 6 = 4(6) + 6 Substitute 6 for x. = 30 Simplify. ASSIGNMENT #6 • • • • • • • • Pg. 24 #9-10 #17-18 Pg. 24 #1-7 odd #11-15 odd Pg. 27 #53-58 all