Suppose that A, B, C, D and A′, B′, C′, D′ (in those orders) form the vertices of convex quadrilaterals. We shall say that the convex quadrilaterals ABCD and A′B′C′D′ are classically congruent if the lengths of the corresponding sides and the measures of the corresponding angles are equal. Show that two parallelograms are classically congruent if |AB| = | A′B′|, | ∠ABC| = | ∠ A′B′C′| and |BC| = |B′C′|.

Q: Prove that for any two points A and B, line segment AB = line segment BA

A: To prove that for any two points A and B, line segment AB = line segment BA.

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Q: Prove that the angle sum of any convex quadrilateral is less than or equal to 360.

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Q: . If a parallelogram has four equal sides and diagonals that are perpendicular to each other, then…

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Q: How many possible nonzero distances does a quadrilateral, that is not a rectangle, rhombus,…

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Q: Let A=(1,2,3), B=(3,4,3), C=(1,4,4) and D=(2,2,5) vertices of a parallelepiped in space and suppose…

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Q: ABCD is a rhombus. If m<ABD = 47o , find m<BAC

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Q: A quadrilateral has vertices Q (-2, -2), R (0, 2), S (4, 3), and T (3,-1). Which statement about…

A: Solution: The objective is to determine the statement about quadrilateral QRST

Q: Suppose that two lines are cut by a transversal in such a way that the pairs of corresponding angles…

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Q: Prop. 43: For every parallelogram, the complements of the parallelograms about the diameter are…

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Q: Select all the statements that would show that quadrilateral ABCD on the coordinate plane is a…

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Q: -5

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Q: Prove that the diagonals of a parallelogram bisect each other.

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Q: Which of the following statements must be true in order to prove that a quadrilateral is a…

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Q: If one diagonal of a cyclic quadrilateral is 18.76 m, with side a = 16.44 m , b = 12.34, c = 10.49,…

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Q: prove that the midpoints of the sides of a quadrilateral of the mice are vertices of a…

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Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: 2. Write two column proofs to prove quadrilateral RSTU is a parallelogram using two separate…

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Q: Given the quadrilateral RSTU with vertices R(5, -3), 5(9, 0), 7(3, 8),and U(-l, 5). a. Show that…

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Q: (4) Prove that if two altitudes in a triangle are congruent, then the triangle is Isosceles.

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Q: 11. The points P(-2, 1), Q(-6, 4), and R(4, 3) are three vertices of parallelogram PQRS. a) Find the…

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Q: acuce 4. Given J(5, 0), K(8, –11), L(-3, –14), M(-6, –3), determine whether parallelogram JKLM is a…

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Q: Prove that a quadrilateral can be inscribed in a circle if and only if its opposite angles are…

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Q: Given any convex quadrilateral (works with concave too, but you only need to prove for convex),…

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Q: what is the length of segment AB with points A(2,4) and B(3,6).  Use √ if necessary.

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A: We prove, opposite sides are equal or congruent in lenth.