6.1 Chords And Arcs

Jan 12, 20100 likes375 views

The document provides instructions and information for an upcoming geometry chapter on circles, noting that it will be a difficult chapter requiring review of vocabulary terms and practice switching between different circle concepts. Students are warned to do their own work and that the teacher will spend extra time reviewing this chapter due to its challenges. Examples are given of different angle types in circles like central angles and inscribed angles as well as properties of chords, arcs, and the relationship between chords and the circle's center.

GEOMETRY Warm Up:
Complete pg. 70 # 1-8 and # 10 (refreshing
your memory)

#1-8 #10

Will be around to collect reflection questions

BEFORE we begin chapter 6......
--MUST KNOW VOCAB!

-Hard chapter
-Will try to review as much as possible
-Will spend more time on this chapter
-Will NOT give extra time on chapter if you act
like fools

-DO YOUR OWN WORK!!!!
-Visually you have to be able to switch back
and forth with vocabulary to see what it is
asking.

What do you see here.....

You will be able to go back and forth- it
takes practice!!!

There are two types of angles in circles:

-Central Angles --vertex is the center of the circle
--measure < is ≅ to the arc it touches
--made up of 2 radii
--DO NOT use ≅ marks on the circle

65° radii

65°
vertex

arc in question

Inscribed angles:
-vertex is ON the circle
-sides made up of chords
-measure < is half of the arc it touches

chords

114°

57°
vertex

arc in question

Chords and arcs:
-if 2 chords are ≅ then the arcs they intercept are ≅
ΑΝD the central angles are ≅

42° 42°

42°
42°

chords

Chords and the center of a circle:
-the perpendicular from the center to a chord
bisects the chord
-if you go backwards and say the perp bisector
passes through the center
-also 2 ≅ chords are equidistant from the center

radius

chord
2 chords that are ≅ therefore they are
the same distance from center (orange)

Try some more....

http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch11/11-02/PH_Geom_ch11-
02_Gizmo.html

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The document discusses different types of polygons and their number of sides and angles, including triangles, quadrilaterals, pentagons, hexagons, octagons, decagons, and dodecagons. It also contains words related to circles like diameter, chord, secant, radius, and central angle scattered throughout a word search grid. Finally, it describes parts of a circle like radius, diameter, chord, secant, point of tangency, arc, and defines central angle and inscribed angle.

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This document defines and explains several circle theorems and properties. It defines key circle terms like diameter, radius, chord, arc, tangent, and segment. It then explains four properties of angles in circles: (1) angles subtended by the same chord or arc in the same segment are equal; (2) if two angles stand on the same chord, the angle at the center is twice the angle at the circumference; (3) the angle in a semi-circle is a right angle; and (4) opposite angles in a cyclic quadrilateral add up to 180 degrees. It also defines properties of tangents to circles, such as tangents being perpendicular to radii and tangents from an outside point being equal.

Circle theoremsOlaug S

6.2 Tangentsjdrambo

The document discusses properties of tangents to circles. It defines a tangent as a line that touches a circle at only one point, called the point of tangency. It describes two key properties: 1) the tangent forms a 90 degree angle with the radius at the point of tangency, and 2) when two tangents are drawn from the same exterior point, the segments of the tangents between that point and the circle are congruent. It also mentions that kite-circle problems frequently involve applying these tangent properties.

Reflection Piece Hwjdrambo

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Hw Ans 5.6 And Chapter 5 Reviewjdrambo

Extra Creditjdrambo

5.1 And 5.2 Rambo Notesjdrambo

The document summarizes key formulas and concepts for calculating angle measurements of polygons: 1) The formula for calculating the sum of the interior angles of any polygon with n sides is 180°(n-2). 2) The sum of the exterior angles of any polygon will always be 360° because if the vertices are pulled into the center it forms a circle. 3) For a regular polygon, the measurement of each interior angle can be calculated by taking the formula 180°(n-2) and dividing by n. The document provides examples of calculating interior, exterior, and total angle measurements using these formulas.

5.5 And 5.6 Rambo Notesjdrambo

The document provides information about properties of parallelograms, rhombuses, rectangles, and squares. It states that parallelograms have opposite angles and sides that are equal, and diagonals that bisect each other. Rhombuses additionally have diagonals that are perpendicular bisectors of each other and that bisect the angles, dividing the rhombus into four equal right triangles. Rectangles have diagonals that are congruent and two lines of reflectional symmetry. Squares have four 90 degree angles and diagonals that bisect each other and the angles, dividing the square into four equal isosceles triangles of 45, 45, 90 degrees.

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The document provides information about properties of kites, trapezoids, triangles, and midsegments. It defines key properties such as: - Kites have two pairs of congruent adjacent sides and perpendicular diagonals. - Trapezoids have one pair of parallel sides and two sets of supplementary angles. Isoceles trapezoids have congruent base angles. - Midsegments of triangles and trapezoids are parallel to the third side and have a length that is half of the third side. - Triangles can be divided into smaller congruent triangles using midsegments.

Ch. 5 Notesjdrambo

Students will be taking notes on Chapter 5 of their geometry textbook. They are to read the chapter sections and complete any investigations or gold boxes. They should take notes on each section separately so additional class notes can be added. Students will make a chart comparing the properties of kites, trapezoids, isosceles trapezoids, parallelograms, rectangles, squares, and rhombi including their side lengths, angle measures, parallel parts, and diagonals. The class will have the option to learn the material through the teacher or by being assigned into groups to teach sections to each other.

Slope Parallperpjdrambo

Review Ch. 4jdrambo

Review 4.5&4.6& Even Hwjdrambo

4.4 And 4.5 Congruencejdrambo

This document provides an overview of congruence shortcuts for triangles. It discusses the different ways triangles can be proven congruent, including: - SAS (Side-Angle-Side) - ASA (Angle-Side-Angle) - SSS (Side-Side-Side) - AAA (Angle-Angle-Angle) It explains that triangles are congruent if three parts (sides or angles) correspond and are equal in measure. The order of the parts must also match between the two triangles.

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Review 4.1 To 4.2jdrambo

The document provides instructions for students to complete a geometry worksheet without writing on it, instead copying problems into notes to help review for an upcoming quiz. Students are told to solve each problem to the best of their ability as the worksheet will be collected and reviewed in class, and that the quiz on Thursday will cover sections 4.1 to 4.2 and include questions from worksheets on those sections.

Hw Answers 4.1 And 4.2jdrambo

4.2 Special Trianglesjdrambo

This document discusses properties of isosceles and equilateral triangles. It reminds the reader that isosceles triangles have two equal sides and two equal angles, and equilateral triangles are a special type of isosceles triangle that has three equal sides and three equal angles. The document emphasizes that isosceles and equilateral triangles have predictable angle and side properties that can be useful for solving problems, especially on standardized tests.

4.1 Triangle Sumjdrambo

This document provides geometry warm up problems focusing on triangle sum conjecture. It reviews that triangles have three sides and three angles. It asks students to recall that the sum of the angles in a triangle is always 180 degrees from prior investigation on page 199. Students are instructed to do a paragraph proof on page 200 using this information. The document also discusses using one triangle to find a missing angle in another triangle, and emphasizes that the order of angles matters.

Chapter 3 Notesjdrambo

This document contains summaries of geometry concepts and homework problems from two different pages in a geometry textbook. It defines key terms like segment bisector, perpendicular bisector, median, midsegment, altitude, angle bisector, concurrent lines, incenter, circumcenter, orthocenter, centroid. It also summarizes how to construct parallel lines and solve specific homework problems from pages 36, 134 and 186 in the geometry book.

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6.1 Chords And Arcs

1. GEOMETRY Warm Up: Complete pg. 70 # 1-8 and # 10 (refreshing your memory) #1-8 #10 Will be around to collect reflection questions

2. BEFORE we begin chapter 6...... --MUST KNOW VOCAB! -Hard chapter -Will try to review as much as possible -Will spend more time on this chapter -Will NOT give extra time on chapter if you act like fools -DO YOUR OWN WORK!!!! -Visually you have to be able to switch back and forth with vocabulary to see what it is asking.

3. What do you see here..... You will be able to go back and forth- it takes practice!!!

4. There are two types of angles in circles: -Central Angles --vertex is the center of the circle --measure < is ≅ to the arc it touches --made up of 2 radii --DO NOT use ≅ marks on the circle 65° radii 65° vertex arc in question

5. Inscribed angles: -vertex is ON the circle -sides made up of chords -measure < is half of the arc it touches chords 114° 57° vertex arc in question

6. Chords and arcs: -if 2 chords are ≅ then the arcs they intercept are ≅ ΑΝD the central angles are ≅ 42° 42° 42° 42° chords

7. Chords and the center of a circle: -the perpendicular from the center to a chord bisects the chord -if you go backwards and say the perp bisector passes through the center -also 2 ≅ chords are equidistant from the center radius chord 2 chords that are ≅ therefore they are the same distance from center (orange)

9. Try some more.... http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch11/11-02/PH_Geom_ch11- 02_Gizmo.html

6.1 Chords And Arcs

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6.1 Chords And Arcs