# annotated-ma722_unit2_section1 (1).pdf - Stan Oleynik...

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Stan OleynikAssignment 3 - Unit 2 Section 1 Assignment Discussion - Problem 2 on page 49MA 722 Spring 2019page 43, problem 3:What can be inferred from Theorem 31 concerning the fourth angle of a Lambert quadri-lateral? Prove it.Statement:We can infer that the fourth angle is not obtuse.1. ConsiderABCD- Lambert quadrilateral, thus]A=]B=]C= 902. Draw a lineACby postulate 1.3. The angle-sum of4ABCis180and the angle-sum of4ADCis180by theorem 31.4. Thus,]2 +]D+]4 +]1 +]3 +]B180+ 180]A+]B+]C+]D360]D+ 270360]D90That is the fourth angle of Lambert quadrilateral is not obtuse.
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page 43, problem 4:Prove that the angle-sum of a quadrilateral does not exceed360.Proof:1. Let’s considerABCD- quadrilateral (as agreed in subdivision properties 9 on page 38 -ABCDis an arbitrary convex quadrilateral).2. Draw a lineACby postulate 1.3. The angle-sum of4ABCis180and the angle-sum of4ADCis180by theorem 31.4. Thus,]2 +]D+]4 +]1 +]3 +]B180+ 180]A+]B+]C+]D360That is the angle-sum of a quadrilateral does not exceed360.
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page 43, problem 5:Prove that two quadrilaterals are congruent if a side, angle, side, angle, side of one areequal to the corresponding parts of the other. The five parts in each case being consecutiveon the quadrilateral.Proof:1. Let’s considerABCDandA1B1C1D1- quadrilaterals, whereAD=A1D1,]A=]A1,AB=A1B1,]B=]B1,BC=B1C1
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