Proving Angle Relationships Postulate 2.10 – Protractor Postulate Given ray AB and a number r...
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![Page 1: Proving Angle Relationships Postulate 2.10 – Protractor Postulate Given ray AB and a number r between 0 and 180, there is exactly one ray with endpoint.](https://reader036.fdocuments.us/reader036/viewer/2022071718/56649ec05503460f94bcbf10/html5/thumbnails/1.jpg)
Proving Angle Relationships
Postulate 2.10 – Protractor Postulate
• Given ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A extending on either side of ray AB, such that the measure of the angle formed is r.
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Proving Angle Relationships
Postulate 2.11 – Angle Addition Postulate
• If R is in the interior of PQS, then mPQR + mRQS = m PQS.
• If mPQR + mRQS = mPQS, then R is in the interior of PQS.
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Answer: 50
QUILTING The diagram below shows one square for a particular quilt pattern. If and is a right angle, find
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Proving Angle Relationships
Theorem 2.3 – Supplement Theorem
• If two angles form a linear pair, then they are supplementary angles.
Theorem 2.4 – Complement Theorem
• If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
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Answer: 28
are complementary angles and .
andIffind
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Proving Angle Relationships
Theorem 2.5 – Angle Congruence Theorem
Congruence of angles is reflexive, symmetric, and transitive.
Reflexive: 1 1
Symmetric: If 1 2, then 2 1.
Transitive: If 1 2 and 2 3, then 1 3.
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Proving Angle Relationships
Theorem 2.6• Angles supplementary to the same angle or to
congruent angles are congruent.Theorem 2.7• Angles complementary to the same angle or to
congruent angles are congruent.Vertical Angles Theorem• If two angles are vertical angles, then they are
congruent.
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In the figure, NYR and RYA form a linear pair,AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that RYN and AXY are congruent.
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Proof:
Statements Reasons
1. Given
2. If two s form a linear pair, then they are suppl. s.
3. Given
4.
1.
2.
3.
4.
linear pairs.
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Answer: mA = 52; mZ = 52
find andIf and are vertical angles and and
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Proving Angle Relationships
Theorem 2.9• Perpendicular lines intersect to form four
right angles.Theorem 2.10• All right angles are congruent.Theorem 2.11• Perpendicular lines form congruent adjacent
angles.
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Proving Angle Relationships
Theorem 2.12
• If two angles are congruent and supplementary, then each angle is a right angle.
Theorem 2.13
• If two congruent angles form a linear pair, then they are right angles.