This is a postulate, not a theorem

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Presentation transcript:

This is a postulate, not a theorem congruent (This was Euclid's 4th postulate) Given ∠K and ∠L are right angles Right Angles Congruence Postulate

congruent ∠1 ≅ ∠3 congruent ∠4 ≅ ∠6

Given ∠2 ≅ ∠4 Definition of congruent angles Given m∠4 = 45°

No, you cannot prove that ∠K and ∠L are right angles because the converse of the Right Angles Congruence Postulate is not always true. No, ∠B and ∠C are complements by the Congruent Complements Theorem, so they cannot be supplements.

supplementary 180° congruent

Given m∠4 = 90° Vertical Angles Congruence Theorem m∠2 = m∠4 Substitution Property of Equality ∠2 and ∠4 are supplementary

m∠1 + m∠4 = 180° m∠1 + 63° = 180° m∠1 = 117° m∠2 = m∠4 m∠2 = 63° m∠1 = m∠3 m∠1 = 121° m∠2 + m∠3 = 180° m∠2 + 121° = 180° m∠2 = 59° m∠2 = m∠4 59° = m∠4

180° 180° 112 180 68 112 17 17 17 17 68 67°

m∠AEB = m∠DEC 4x - 18 = 3x + 4 x - 18 = 4 x = 22 m∠AEB = 4x - 18 m∠AEB = 4(22) - 18 m∠AEB = 70°