Geometry Notes Intro to Geo Proofs - 2: Angles. 2. (Sometimes) by a single letter at the vertex (only if there is no chance of confusion),
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1 Name: ate: Geometry Notes Intro to Geo roofs - 2: ngles efinitions (continued) n angle is the union of two rays with a common endpoint (the vertex). NTE: ngles may be named in three ways. 1. y three letters, with the middle letter at the vertex, 2. (Sometimes) by a single letter at the vertex (only if there is no chance of confusion), 3. y a number or lower case letter placed inside the angle near the vertex. Ex: In the diagram at right, The measure of an angle is the number of degrees in the angle. Note: The measure of an angle is a measure of rotation (turning). It has nothing to do with the lengths of the sides. cute angle: 50 Right angle: btuse angle: Straight angle: ongruent angles: Two angles that have the same measure. F J
2 erpendicular segments (or lines or rays) Ex: Given and, m = 3x + 20 and m = 5(x 2). etermine if. Two angles are complementary if their measures Two angles are supplementary if their measures Ex: The measures of two complementary angles are in the ratio 3:5. Find the measure of the larger angle. Two adjacent angles share a common ray but have no interior points in common.
3 ngle bisector: ray that divides an angle into two congruent angles. ostulate: Every angle has exactly one bisector. Ex: H, m HT = 5x + 3 and m T = 2x oes T bisect H? H T 5x + 3 2x + 28
4 Name: ate: Geometry Homework: Intro Geo roofs Use the diagram at right to answer the following. a. How many angles in the diagram have their vertex at? b. How many angles in the diagram have their vertex at? c. What angle (number) is named? d. Name two adjacent angles in the diagram. e. re and adjacent? f. Give three alternate names for 4. g. Explain why we should not refer to in the diagram. (Yes, you may lose points for sloppy notation on quizzes and tests.) h. Name one acute angle on the diagram. i. Name one obtuse angle on the diagram. j. Which angle on the diagram appears to be closest to a right angle? R 2. In the diagram at right, which angle has a larger measure, Q or RS? Q S 3. In the diagram at right, N, R Q, and m Q = 40. Find m NR. N Q R
5 4. The measures of two supplementary angles are in the ratio 5:7. Find the measure of the smaller angle. 5. The measure of the complement of an angle is 18 less than twice the measure of the angle. What is the numerical measure of the angle? 6. If ET bisects EG, m ET = x 2 and m GET = 5x + 14, find the numerical measure of EG. 7. If Y bisects T, m Y = 3x + 8 and m T= 8x 2, find the numerical measure of TY.
6 RE: Remember from the last assignment: Numbers can always be added and subtracted. It makes no sense to add or subtract people. Line segments can sometimes be added or subtracted (if you don t remember when, review the note after homework I 1 #5). ngles are like segments. They can sometimes be added and subtracted. Remember, represents an actual angle (a geometric object); m is a number that represents the degree measure of. Your answers to #8 should have been Yes for all except parts b and f. 1) dding two angles only makes sense if they are adjacent: they share a vertex and one side but have no interior points in common (one is not inside the other). + = + = nonsense + = nonsense + = nonsense 2) Subtracting two angles only makes sense if they share a vertex and one side and the second side of the smaller angle is on the interior of the larger angle (the smaller angle is part of the larger angle). = = nonsense = nonsense = = nonsense
7 8. ased on the diagram at right, tell if each of the following is True or False. Remember the difference between and m. 55 a. m + m = m b. + = c. m + m = m d. + = e. m m = m f. = g. m m = m h. = 9. Use the diagram at right to fill in an appropriate angle for each of the following or write nonsense. N S G a. NG + LG = b. SEG + EL = E c. NS + NSE = d. LGS EGS = e. NSE ESG = f. LG LE = g. LGS + EGS = h. LSN LE = L
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Name: Date: / / Spiral Back: Evaluate the following when x = -2 and y = 3 1) -4y x + (3+ x 2 ) Let s see what you remember! Sticker Challenge! Solve the following equations: 2) x 6 = -20 3) 2x 2 = -16