Download Geo 1-4 Lesson with notes 1st a.notebook

Geo 1­4 Lesson with notes 1st a.notebook
September 10, 2015
1­4 Angle Measure
Learning Targets:
I can classify angles
I can measure angles
I can identify and use congruent angles and the bisector of an angle
When is a miter joint typically used?
If the corner created by the two angles is perfect, what are the angels of the miter cuts?
Do the angles of the miter cuts always measure 45 ? Explain.
Aug 26­12:20 PM
Sep 4­8:02 AM
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Geo 1­4 Lesson with notes 1st a.notebook
September 10, 2015
Ray: part of a line, it has one endpoint and extends indefinitely in one direction. Named by endpoint and another point on the ray with the ray symbol.
It cannot be named as OM because O is not the endpoint.
Opposite rays: two collinear rays that share a common endpoint. They form a line.
Angle: formed by two noncollinear rays that have a common endpoint. The rays are called sides of the angle and the common endpoint is the vertex. Named by three capital letters, the middle being the vertex or a number or a single capital letter only when there is exactly one angle at the vertex.
<X, <YXZ, <ZXY, or <3
An angle divides a plane into three distinct parts.
Points Q, M, and N lie on the angle
Points S and R lie in the interior of the angle
Points P and O lie in the exterior of the angle
Jul 26­4:58 PM
Example 1: 1. Name all angles that have B as a vertex.
2. Name the sides of <5.
3. Write another name for <6.
4. What is the vertex of <5?
5. Name the sides of <5.
6. Write another name for <ECL.
7. Name a point in the exterior of <CLH.
Jul 26­5:11 PM
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Geo 1­4 Lesson with notes 1st a.notebook
September 10, 2015
Degree results in dividing a circle into 360 parts.
Jul 26­5:30 PM
Example 2:
8. Copy the diagram below, and extend each ray. Classify each angle as right, acute, or obtuse. Then use a protractor to measure the angle to the nearest degree.
Jul 26­5:37 PM
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Geo 1­4 Lesson with notes 1st a.notebook
September 10, 2015
Copy the diagram below, and extend each ray. Classify each angle as right, acute, or obtuse. Then use a protractor to measure the angle to the nearest degree.
9. <AFB
10. <CFA
11. <AFD
12. <CFD
Jul 26­5:42 PM
Congruent angles: angles that have the same measure
Since m<ABC = m<FED, then <ABC ≅ <FED
Matching numbers of arcs indicate congruent angles
<CBE ≅ <DEB
Angle bisector: a ray that divides an angle into two congruent angles
If YW is the angle bisector of <XYZ, then point W lies in the interior of <XYZ and <XYW ≅ <WYZ
m<XYW + mWYZ = m<XYZ
part + part = whole
whole ­ part = part
Jul 26­5:45 PM
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Geo 1­4 Lesson with notes 1st a.notebook
September 10, 2015
Example 3:
13. Wall stickers of standard shapes are often used to provide a stimulating environment for a young child's room. A five­pointed star sticker is shown with vertices labeled. Find m<GBH and m<HCI if <GBH ≅ <HCI, m<GBH = 2x + 5, and m<HCI = 3x ­ 10.
Jul 26­6:04 PM
14. Suppose m<JKL = 9y + 15 and m<JKN = 5y + 2. Find m<JKL.
Jul 26­6:09 PM
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