Geo (H) 2.8 Proving Angle Relationships.notebook
2.8 Proving Angle Relaonships
Objecves: 1. You will analyze given statements and diagrams to write proofs about angle addion and angle congruence. Postulate 2.10: Protractor Postulate measure of an angle corresponds to a pos real #
Postulate 2.11: Angle Addion Postulate if D is in the interior of <ABC, then m<ABD + m<DBC = m<ABC.
Theorem 2.3: Supplement Theorem If 2 angles form a linear pair, then they are supplementary angles.
Theorem 2.4: Complement Theorem If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary angles. Theorem 2.5: Properes of Angle Congruence
Reflexive Property of Congruence: <A <A
Symmetric Property of Congruence:If <A <B, then <B <A.
Transive Property of Congruence : If <A <B and <B <C, then <A <C.
Theorem 2.6: Congruent Supplements Theorem Angles supplementary to the same angle or to congruent angles are congruent.
Theorem 2.7: Congruent Complements Theorem Angles complementary to the same angle or to congruent angles are congruent.
Theorem 2.8: Vercal Angles Theorem : If 2 angles are vercal angles, then they
are congruent. Right Angle Theorems
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.
Theorem 2.12: If 2 angles are & supplementary, then each angle is a right angle. Theorem 2.13: If 2 angles form a linear pair, then they are right angles. Geo (H) 2.8 Proving Angle Relationships.notebook
Example 1:
Given: ∠1 and ∠ form a linear pair
m∠3 +m ∠1 = 180
Prove: ∠3 ≅ ∠4 Geo (H) 2.8 Proving Angle Relationships.notebook
Example 2:
If ∠1 and ∠2 are vercal angles and m∠1 = d – 32 and m∠2 = 175 – 2d, find m∠1 and m∠2. Jusfy each step.
Geo (H) 2.8 Proving Angle Relationships.notebook
Example 3:
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 ∠NYR and ∠AXY are congruent.
Statement
1. ∠NYR and ∠RYA form a Reason
1. Given
linear pair, ∠AXY and ∠AXZ form a linear pair, and ∠RYA and ∠AXZ are congruent 2. ∠NYR and ∠RYA are supplementary, ∠AXY and ∠AXZ are supplementary 2. definition of linear pair
3.∠NYR + ∠RYA = 180
3. definition of supplementary agles
4. ∠NYR + ∠RYA = ∠AXY + ∠AXZ
4. substitution
5. ∠RYA = ∠AXZ 5. definition of congruent angles
6. ∠NYR + ∠AXZ = ∠AXY + ∠AXZ 6. substitution
7. ∠NYR = ∠AXY
7. subtraction property of equality
8. ∠NYR ≅ ∠AXY
8. definition of congruent angles
∠AXY + ∠AXZ =180
Geo (H) 2.8 Proving Angle Relationships.notebook
Example 4:
Given: ∠1 and ∠3 are complementary
∠2 and ∠3 are complementary
Prove: ∠1 ≅ ∠2 Geo (H) 2.8 Proving Angle Relationships.notebook
2.8 p.156
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