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Transcript
Proofs Check out the interactive quiz, Chapter 2, “Videos & Activities”. Also see page S82+ for complete listing of theorems, postulates, etc. OR use your “cheat sheet”! KL MN and KLM MNK. Determine if the quadrilateral must be a parallelogram. Justify your answer. a. No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met. b. Yes. Opposite angles are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram. c. Yes. Opposite sides are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram. d. Yes. One set of opposite sides are congruent, and one set of opposite angles are congruent. This is sufficient evidence to prove that the quadrilateral is a parallelogram. Which of these could BEST be used to demonstrate the vertical angle theorem? a. b. scissors thermometer c. d. drawing compass protractor For a homework assignment about quadrilaterals inscribed in a circle, Gloria drew the diagram shown below. She wrote the following step in a proof. m S 1 2 mPQR and m Q 1 2 mPSR because the measure of an angle inscribed in a circle is one-half the measure of the intercepted arc. Based on this diagram and the beginning of Gloria’s proof, which of the following is a true conclusion that Gloria could prove? a. The opposite angles of an inscribed quadrilateral are congruent. b. The opposite angles of an inscribed quadrilateral are right angles. c. The opposite angles of an inscribed quadrilateral are complementary. d. The opposite angles of an inscribed quadrilateral are supplementary. Given: AB GH; AC FH; AC FH Prove: ABC HGF a. 1. Alternate Exterior Angles Theorem 2. Alternate Interior Angles Theorem c. 1. Alternate Exterior Angles Theorem 2. Alternate Exterior Angles Theorem b. 1. Alternate Interior Angles Theorem 2. Alternate Exterior Angles Theorem d. 1. Alternate Interior Angles Theorem 2. Alternate Interior Angles Theorem Write a justification for each step to prove EF = GH, given that EG = FH. Identify the property that justifies the statement: AB CD and CD EF so AB EF a. b. c. d. Reflexive Property of Congruence Symmetric Property of Congruence Substitution Property of Congruence Transitive Property of Congruence