TechMathI - 1.3
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The document provides information and examples about classifying and calculating angles using angle addition and vertical angles. It defines acute, right, obtuse and straight angles. It then gives examples of finding missing angle measures using angle addition or that vertical angles are equal.
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Some slides lifted from: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CEsQFjAD&url=http%3A%2F%2Fdionmath.wikispaces.com%2Ffile%2Fview%2F2.3%2BComplementary%2Band%2BSuppl.%2BAngles.ppt&ei=_wVFUbzHCa-o4AP9ooGwBQ&usg=AFQjCNF-KDyDx_yiVaUuMJMdM6yOJqHASQ&sig2=wH2TZ9xGxsHgtc4cCnn2QQ&bvm=bv.43828540,d.dmg&cad=rja
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Identify
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and set up and solve equations.
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Classify triangles by sides and by angles.
Find the measures of missing angles of right and equiangular triangles.
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The document discusses several geometry theorems including:
1. The Triangle Sum Theorem which states that the sum of the interior angles of any triangle is 180 degrees.
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The document provides examples of using these theorems to prove other statements and find missing angle measures in geometric figures. It also assigns practice problems for students.
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This document defines angles and their measures. It discusses that an angle consists of two rays with a common vertex point. The measure of an angle is denoted by m∠ and can be approximated using a protractor in degrees. Angles with the same measure are congruent. The document also covers classifying angles as acute, right, obtuse, or straight based on their measure. Additionally, it discusses adjacent angles and the angle addition postulate.
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The document provides information about geometry, specifically angles of triangles. It discusses the triangle angle sum theorem, which states that the sum of the interior angles of any triangle is 180 degrees. It provides examples of using this theorem to find missing angle measures in triangles. It also covers exterior angles and their relationships to interior angles, including theorems such as the exterior angle theorem. The document aims to teach students about important angle properties and relationships in triangles through definitions, theorems, and worked examples.
Obj. 8 Classifying Angles and Pairs of Angles
The student will be able to (I can):
Correctly name an angle
Classify angles as acute, right, or obtuse
Identify
linear pairs
vertical angles
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supplementary angles
and set up and solve equations.
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This document discusses the inscribed angle theorem and its corollaries. The inscribed angle theorem states that if an angle is inscribed in a circle, then its measure is half the measure of the intercepted arc. Two corollaries are provided: 1) any angle inscribed in a semicircle is a right angle, and 2) every two angles inscribed in the same arc are congruent. Several examples demonstrate using the theorem and corollaries to solve for unknown angle measures.
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This document defines and provides properties of arcs, chords, circles, and related geometric terms like radius, diameter, tangent, and secant. It includes theorems about lines that are tangent or perpendicular to a circle. Examples demonstrate finding measures of arcs and angles, as well as using properties of tangents, radii, and chords to solve for variable values.
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The document discusses several theorems related to triangles:
1) The triangle inequality theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than their difference.
2) The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the remote interior angles.
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3. The third lesson generalizes these rules to any polygon with n sides, teaching that the sum of interior angles is (n-2)*180 degrees and the sum of exterior angles is always 360 degrees.
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TechMathI - 1.3
- 3. Name whether each is an acute, right, obtuse or straight angle.
- 4. Angle Addition m < BAD = 16 ° m < CAD = 38° OR m < 1 = 16° m < 2 = 38° What is the measure of <CAB? A C D B 2 1
- 5. Angle Addition 1) 2) m < CAD = 21 ° m < DAB = 42° Find <CAB m < 3 = 59° m < 4 = 52° Find < 3 + <4 X A C D B 2 1 W Y Z 3 4
- 6. Angle Addition 3) 4) m < CAD = 11 ° m < CAB = 62° Find <DAB m < 3 = 49° m < 3 + 4 = 102° Find m <4 X A C D B 2 1 W Y Z 3 4
- 7. You try! 1) 2) m < DAB = 54 ° m < CAB = 80° Find <DAB m < 3 + 4 = 119° m < 4 = 42° Find m <3 X A C D B 2 1 W Y Z 3 4
- 8. Vertical Angles “ across from” m <1 = m <3 AND m <2 = m <4 2 3 4 1
- 9. You try! Find the measures of angle 1 and 2. 42 ° 138 ° 2 1
- 10. W X Y Z Given: m<XWZ = 75 ° m<1 = 2x + 5 m<2 = x – 2 Find measure of <1 and < 2. 1 2
- 11. W X Y Z Given: m<XWZ = 115 ° m<1 = x + 12 m<2 = 2x – 2 Find measure of <1 and < 2. 1 2
- 12. W X Y Z Given: m<1 = 62 ° m<2 = x + 11 m<1 + 2 = 90 Find measure of <1 and < 2. 1 2