3.2 proof and perpendicular lines. let’s review theorem 2.6-vertical angles theorem vertical...
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3.2 Proof and Perpendicular Lines
Let’s Review
Theorem 2.6-Vertical Angles Theorem• Vertical angles are
congruent….• Given: <5 & <6 are a linear
pair; <6 & <7 are a linear pair.
• Prove: m<5=m<7
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5
Statement Reason1. <5 & <6, <6 &<7 are a linear pair
1. Given
2. <5 & <6, <6 & <7 are supplements
2. Linear Pair Postulate
3. m<5=m<7 3. Congruent Supplements Theorem
Theorem 3.1 (p137)
• If two lines intersect to form a linear pair of congruent angles,
• Then the lines are perpendicular.
gh
h
g
Theorem 3.2
• If two sides of two adjacent acute angles are perpendicular,
• Then the angles are complementary.
Theorem 3.3
• If two lines are perpendicular,
• Then they intersect to form four right angles. 90
90
90
90
State the Reason for the Conclusion:
State the Reason for the Conclusion:
State the Reason for the Conclusion:
State the Reason for the Conclusion:
State the Reason for the Conclusion:
Find the value of x:
Find the value of x:
Find the value of x:
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