3.2 Proof and Perpendicular Lines

WHY?

PROVE!

Different Kinds of Mathematical Proofs Two-Column Proofs (Section 2.6) Paragraph Proofs Flow Proofs

5 6 7 Given: <5 and <6 are a linear pair. <6 and <7 are a linear pair. Prove: <5 is congruent to <7 2-Column Proof ReasonsStatements

5 6 7 Given: <5 and <6 are a linear pair. <6 and <7 are a linear pair. Prove: <5 is congruent to <7 ReasonsStatements 1.<5 and <6 are a linear pair. <6 and <7 are a linear pair. 2.<5 and <6 are supplementar y. <6 and <7 are supplementar y. 3. <5 is congruent to <7 1.Given. 2.Linear Pair Postulate. 3.Congruent Supplements Theorem Because <5 and <6 are a linear pair, the linear Pair Postulate says that <5 and <6 are supplementary. The same reasoning shows that <6 and <7 are supplementary. Because <5 and <7 are both supplementary to <6, the Congruent Supplements Theorem says that <5 is congruent to <7

5 6 7 Given: <5 and <6 are a linear pair. <6 and <7 are a linear pair. Prove: <5 is congruent to <7 ReasonsStatements 1.<5 and <6 are a linear pair. <6 and <7 are a linear pair. 2.<5 and <6 are supplementary. <6 and <7 are supplementary. 3. <5 is congruent to <7 1.Given. 2.Linear Pair Postulate. 3.Congruent Supplements Theorem FLOW PROOF <5 and <6 are a linear pair. <5 is congruent to <7. <6 and <7 are supplementary. <5 and <6 are supplementary. <6 and <7 are a linear pair. Given. Linear Pair Postulate. Congruent Supplements Theorem.

If I had two lines that intersect to form a linear pair of congruent angles then what do we know about them?

Theorem 3.1 (pg. 135) If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. h g

h g 21 Given: <1 is congruent to <2. <1 and <2 are a linear pair. Prove: g is perpendicular to h <1 and <2 are a linear pair. <1 and <2 are supplementary. <1 is a right < 2(m<1)=180 m<1 = m<2 m<1 = 90 m<1 +m<2 = 180 <1 is congruent to <2 FLOW PROOF m<1 +m<21= 180 g is perp. to h Given. Linear Pair Postulate Def. of Supplementary <s Substitution prop of equality Def. of congruent angles. Distributive prop. Def of perp. linesDef. of right angle Div. prop. Of equality

If two sides of two adjacent acute angles are perpendicular, what does that mean?

Theorem 3.2 (pg. 135) If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

FLOW PROOF Given: <A and <B are adjacent and acute Prove: <A and <B are complementary

If two lines intersect and form four right angles what can you tell me bout the lines?

Theorem 3.3 (pg. 135) If two lines are perpendicular, then they intersect to form four right angles.

End of Lesson Questions 1.Draw the outlines of a two column proof and a flow proof. Make sure to label where the reasons and statements go. 2.What three things were learned about perpendicular lines today? 3.Daily Puzzler (digital clock): “I’m constructed from more than 4 distinct segments. I contain 4 different pairs of parallel segments. I contain 6 different pairs of perpendicular segments.”