(02.06 MC) Look at the quadrilateral shown below: Melissa…
(02.06 MC) Look at the quadrilateral shown below: Melissa writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Melissa’s proof For triangles AOB and COD, angle 1 is equal to angle 2, as they are vertical angles. AO = OC and BO = OD because it is given that diagonals bisect each other. The ________ are congruent by SAS postulate. Similarly, triangles AOD and COB are congruent. By CPCTC, AB is equal to DC. By CPCTC, AD is equal to BC. As the opposite sides are congruent, the quadrilateral ABCD is a parallelogram. Which is the missing phrase in Melissa’s proof?
Read Details(01.07 MC) Daniel is constructing a fence that consists of…
(01.07 MC) Daniel is constructing a fence that consists of parallel sides and . Complete the proof to explain how he can show that m∠GKB = 120° by filling in the missing justifications. Statement Justification ∥ m∠ELJ = 120° Given m∠ELJ + m∠ELK = 180° Linear Pair Postulate m∠BKL + m∠GKB = 180° Linear Pair Postulate m∠ELJ + m∠ELK = m∠BKL + m∠GKB Transitive Property ∠ELK ≅ ∠BKL 1. m∠ELK = m∠BKL 2. m∠ELJ + m∠ELK = m∠ELK + m∠GKB Substitution Property m∠ELJ = m∠GKB Subtraction Property m∠GKB = m∠ELJ Symmetric Property m∠GKB = 120° Substitution
Read Details(02.06 MC) Look at the quadrilateral shown below: Terra wr…
(02.06 MC) Look at the quadrilateral shown below: Terra writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Terra’s proof AO = OC because it is given that diagonals bisect each other. BO = OD because it is given that diagonals bisect each other. For triangles AOB and COD, angle 1 is equal to angle 2, as they are ________. Therefore, the triangles AOB and COD are congruent by SAS postulate. Similarly, triangles AOD and COB are congruent. By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC. As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel. Therefore, ABCD is a parallelogram. Which is the missing phrase in Terra’s proof?
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