chapter 1 basics of geometry - st. joseph high school › cms › lib › il02222025... · chapter...
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Chapter 1
Basics of Geometry
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Section 6Angles and Their Measures
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An __angle__ consists of two rays that have the same endpoint.
The rays are the __sides__ of the angle.
The endpoint is the __vertex__ of the angle.
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In the photograph at the right, the sides of <BAC are AB and AC. The vertex of <BAC is point A.
You can also write <BAC as <CAB. Notice the middle letter in the name of the angle is always the vertex of the angle.
You can write simply <A if there are no other angles that have this same vertex.
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Example 1: Name Angles
Name the angles in the figure.
<PQS (<SQP)
<SQR (<RQS)
<PQR (<RQP)
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Checkpoint: Name Angles
Name the angles in the figure.
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The measure of an angle is written in units called __degrees__.
The measure of <A is denoted by __m<A__.
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Example 2: Measure Angles
Use a protractor to approximate the measure of <BAC.
m<BAC = 50*
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Two angles are __congruent angles__ if they have the same measure. In the diagram below, the two angles have the same measure, so <DEF is congruent to <PQR. You can write <DEF ≅ <PQR.
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Angles are classified as __acute__, __right__, __obtuse__, or __straight__, according to their measures. Angles have measures greater than 0° and less than or equal to 180°.
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Example 3: Classify Angles
Classify each angle.
obtuse right acute
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Example 4: Add Angle Measures
Find the measure of <PTM.
<PTN + <NTM = <PTM
30 + 40 = <PTM
70* = <PTM
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Checkpoint: Add and Subtract Angle Measures
looking for the whole add; looking for the part subtract
Find the measure of <ABC.