Obj. 58 Angle Relationships
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1) If a tangent and secant intersect at the point of tangency, the measure of the angle formed is half the measure of the intercepted arc. 2) If two secants or chords intersect in the interior of a circle, the measure of each angle formed is half the sum of the intercepted arcs. 3) If secants or tangents intersect outside a circle, the measure of the angle formed is half the difference between the intercepted arcs.
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3 analysis
1. The document discusses two methods for analyzing trusses: the method of joints and the method of sections.
2. The method of joints involves satisfying equilibrium conditions at each joint to solve for member forces. The method of sections allows analyzing any member directly by considering equilibrium across a cut through the truss.
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This document defines various circle terms like tangent, secant, concentric circles, and common tangents. It then discusses theorems for finding angle measures based on whether the vertex is on the circle, inside the circle, or outside the circle. For a vertex on the circle, the angle measure is half the intercepted arc. For inside, it's half the sum of intercepted arcs. For outside, it's half the difference of intercepted arcs. Examples are provided to demonstrate applying these theorems to find unknown angle measures.
Lecture 4.1 4.2
The document discusses classifying and finding angles of triangles. It defines different types of triangles based on sides or angles, such as equilateral, isosceles, scalene, acute, obtuse, right. The triangle sum theorem states the sum of interior angles is 180 degrees. The exterior angle theorem relates exterior to interior angles. Examples show using these theorems to find missing angle measures in various triangles.
Geometry unit 12.4
This document provides examples and explanations of how to find angle measures formed by lines intersecting within and on circles. It includes examples of finding angle measures using tangent-secant angles, tangent-chord angles, and angles inside and on circles. Students are guided through step-by-step workings and are given practice problems to solve involving finding specific angle measures using the concepts taught.
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This document contains a lesson plan on trigonometric functions for angles of any measure from a Bridge to Calculus workshop. It includes topics like right triangle trigonometry, angles in standard position, trig functions of common angles, the unit circle, and formulas like the rule of sines and cosines. Examples are provided to illustrate solving right triangles and converting between degree and radian measure.
mathemaics 10 lesson about cicles. its part
grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements.grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corresponding measurements. grade 10 lesson about circle. mathematocs lesson about circles. parts of the circles and the corr
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Obj. 58 Angle Relationships
- 1. Obj. 58 Angle Relationships The student is able to (I can): • Find the measures of angles formed by lines that intersect circles • Use angle measures to solve problems
- 2. If a tangent and a secant (or a chord) intersect at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc. F L • Y LF is a secant. LY is a tangent. ∠ = 1 m FLY mFL 2
- 3. Example Find each measure: 1. m∠EFH 2. 180 — 122 = 58º mGF ∠ = = ° 1 m EFH (130) 65 2 58º = = °mGF 2(58) 116
- 4. If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the intercepted arcs. 1111 G R A D ( )∠ = + 1 m 1 mDG mRA 2
- 5. Example Find each measure. 1. m∠1 2. m∠2 m∠2 = 180 — m∠1 = 180 — 80 = 100º 99º 61º 1 2 ( )∠ = + 1 m 1 99 61 2 = 80º
- 6. If secants or tangents intersect outside a circle, the measure of the angle formed is half the difference between the intercepted arcs. M O N E Y 1 ( )∠ = − 1 m 1 mNY mOE 2
- 7. Example Find each measure 1. m∠K 2. x 186º 62º K 26º 94º ∠ = − 1 m K (186 62) 2 = 62º = − 1 26 (94 x) 2 xº 52 = 94 — x x = 42º