1.6 Angles and Their Measures
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1 1.6 ngles and Their Measures Goal Measure and classify angles. dd angle measures. VOULRY ngle, ides, Vertex n angle consists of two rays that have the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. Measure of an angle, degrees The size of an angle, written in units called degrees ( ). The measure of a is denoted by ma. ongruent angles ongruent angles are angles that have the same measure. cute angle n acute angle is an angle with measure between 0 and 90. Right angle right angle is an angle with measure 90. Obtuse angle n obtuse angle is an angle with measure between 90 and 180. traight angle straight angle is an angle with measure 180. Lesson 1.6 Geometry, oncepts and kills Notetaking Guide 21
2 Example 1 Name ngles Name the angles in the figure. There are three different angles. Q R aq or aq aqr or arq aqr or arq Follow-Up In Example 1, why should you not name any of the angles aq? Q is the vertex of three different angles. The name aq would not distinguish one angle from the others. heckpoint Name the angles in the figure R M G T H K N J F art, atr, ahmk, akmn, agj, ajf, or a ahmn agjf Example 2 Measure ngles Use a protractor to approximate the measure of a. ut the center of the protractor over the vertex point. lign the protractor with one side of the angle. The second side of the angle crosses the protractor at the 50 mark. o, ma Geometry, oncepts and kills Notetaking Guide hapter 1
3 Example 3 lassify ngles lassify each angle. a. ma 130 b. ma 90 c. ma 45 a. a is obtuse because its measure is greater than 90. b. a is right because its measure is 90. c. a is acute because its measure is less than 90. Follow-Up Use your protractor to sketch each angle in Example 3. a a a heckpoint lassify the angle. 4. ma mae maf 173 acute straight obtuse OTULTE 6: NGLE ITION OTULTE Words If is in the interior of art, then the measure of art is the sum of the measures of ar and at. ymbols If is in the interior of art, then mar mat mart. T R Lesson 1.6 Geometry, oncepts and kills Notetaking Guide 23
4 Follow-Up ompare and contrast the ngle ddition ostulate with the egment ddition ostulate in Lesson 1.5. How are they alike? They both allow you to add the measures of geometric figures. How are they different? One adds segment lengths. The other adds angle measures. Example 4 dd ngle Measures Find the measure of atm. N 30 matm matn mantm matm matm 70 nswer The measure of atm is 70. M 40 T ngle ddition ostulate ubstitute angle measures. dd angle measures. heckpoint Find the measure of a Geometry, oncepts and kills Notetaking Guide hapter 1
5 Words to Review Give an example of the vocabulary word. onjecture The product of four consecutive numbers, plus 1, is always a perfect square. oint, line, plane plane line point ostulate Through any two points there is exactly one line. ollinear points,, and are collinear. oplanar points oplanar lines, E, F, and G are coplanar. Lines m, n, and p are coplanar. G E F n p m egment, endpoints Ray &* is a segment with &( is a ray with initial endpoints and. point. Words to Review Geometry, oncepts and kills Notetaking Guide 25
6 Intersect, Intersection oordinate Lines l and k intersect at. The coordinate of is 5. l k 5 istance The distance between and is. Length of a segment The length of &* is. etween oint M is between L and N. ongruent segments &* and &* are congruent. L M N &* c &* ngle, ides, Vertex vertex sides a, a, a Measure of an angle, degrees The measure of a is ma Geometry, oncepts and kills Notetaking Guide hapter 1
7 ongruent angles a and ae are congruent. cute angle 0 < ma < 90 E F a cae Right angle ma 90 Obtuse angle 90 < ma < 180 traight angle ma 180 Review your notes and hapter 1 by using the ummary and Review on pages of your textbook. Words to Review Geometry, oncepts and kills Notetaking Guide 27
1.6 Angles and Their Measures
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Geometry Unit 1 Packet - Language of Geometry Name: #: Video Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruent, parallel, perpendicular, etc.) Term