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2. Prove Theorem 6.2.5: If the diagonals of a parallelogram are perpendic- ular, then the parallelogram...
prove the following 1) 2) 3) 4)A parallelogram is a square iff it's diagonals are perpendicular...
prove the following
1)
2)
3)
4)A parallelogram is a square iff it's diagonals are
perpendicular and congruent.
5) the median of a trapeziod is parallel to each
base
3.7) Corollary (Parallel CT). Let l, and l be coplanar lines and I a transversal. a. (Property C) 4 | l, if and only if a pair of interior angles on the same side of t are supplementary b. (Property T) Ift 1 l and 41 || 12, then t 1...
QUESTION 1 Quadrilateral WXZY is a square. If the measure of angle XYZ = 4x +...
QUESTION 1
Quadrilateral WXZY is a square. If the measure of angle XYZ = 4x
+ 15, find the value of x.
15
15
18.75
7.5
2 points
QUESTION 2
Determine whether parallelogram JKLM with vertices J(-1, 1),
K(4, 1), L(4, 6) and M(-1, 6) is a rhombus, square, rectangle or
all three.
rhombus
square
rectangle
rhombus, square and rectangle
2 points
QUESTION 3
In rectangle JKLM, JK is equal to 12 feet, and LN is equal...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.] 5) Consider the following statements: I: If two triangles are congruent, then they have equal defect. II: If two triangles are similar, then they have...
(2) Follow the steps below to prove Theorem 7.2.8: A bounded function / : [a,b] +...
(2) Follow the steps below to prove Theorem 7.2.8: A bounded function / : [a,b] + R is integrable on (a, b) if and only if Ve > 0, there exists a partition P. of (a,b) such that UC, P.) - LIS, P.) <E. (a) Explain why the existence of the partition P. implies that L(I) = (/), and therefore that is integrable. (b) Conversely, ilis integrable, then there exists partitions P, Q of [a,b] such that UU,P) - L(Q)<E...
prove the following
1)
2)
3)
4)A parallelogram is a square iff it's diagonals are
perpendicular and congruent.
5) the median of a trapeziod is parallel to each
base
3.7) Corollary (Parallel CT). Let l, and l be coplanar lines and I a transversal. a. (Property C) 4 | l, if and only if a pair of interior angles on the same side of t are supplementary b. (Property T) Ift 1 l and 41 || 12, then t 1...
QUESTION 1
Quadrilateral WXZY is a square. If the measure of angle XYZ = 4x
+ 15, find the value of x.
15
15
18.75
7.5
2 points
QUESTION 2
Determine whether parallelogram JKLM with vertices J(-1, 1),
K(4, 1), L(4, 6) and M(-1, 6) is a rhombus, square, rectangle or
all three.
rhombus
square
rectangle
rhombus, square and rectangle
2 points
QUESTION 3
In rectangle JKLM, JK is equal to 12 feet, and LN is equal...
(2) Follow the steps below to prove Theorem 7.2.8: A bounded function / : [a,b] + R is integrable on (a, b) if and only if Ve > 0, there exists a partition P. of (a,b) such that UC, P.) - LIS, P.) <E. (a) Explain why the existence of the partition P. implies that L(I) = (/), and therefore that is integrable. (b) Conversely, ilis integrable, then there exists partitions P, Q of [a,b] such that UU,P) - L(Q)<E...
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